mmi 


THE    WILEY   TECHNICAL   SERIES 

FOR 

VOCATIONAL    AND    INDUSTRIAL    SCHOOLS 

EDITED   BY 

J.    M.    JAMESON 

PRATT   INSTITUTE 


THE  WILEY  TECHNICAL  SERIES 

EDITED  BY 

J.  M.  JAMESON 


(For  full  announcement  see  page  333.) 

THE   ESSENTIALS    OF  ELECTRICITY.     By  W.  H.  TIMBIE,  Wentworth. 

Institute. 

HEAT;  FOR  TECHNICAL  AND  INDUSTRIAL    STUDENTS.     By  J.   A. 

RANDALL,  Pratt  Institute. 

GAS  POWER.      By  Professor  C.  F.  HIKSHFELD  and  T.  C.  ULBBICHT, 
Cornell  University.    (Ready  shortly.) 

CONTINUOUS     AND     ALTERNATING    CURRENT    MACHINERY.   .  By 

Professor  J.  H.  MOBECKOFT,  Columbia  University.     (Ready  shortly.) 

ALTERNATING   CURRENTS.     By  W.    H.    TIMBIE   and  H.  H.  HIQBIE, 

Wentworth  Institute.    (In preparation.) 

HEAT  AND  LIGHT  IN  THE  HOUSEHOLD.     By  W.  G.  WHITMAN,  State 
Normal  School,  Salem,  Mass.    (In preparation.) 

ELECTRIC  LIGHTING.     By  H.  H.  HIGBIE,  Wentworth  Institute.     (In 
preparation.) 

PATTERN  MAKING.    By  FREDERICK  W.  TURNER  and  DANIEL  G.  TOWN, 
Mechanics  Arts  High  School,  Boston.     (In preparation.) 

DRAFTING  AND  DESIGN.    By  CHARLES  B.  HOWE,  Stuyvesant  Technical 
Hign  School,  New  York,  and  associated  specialists, 
(a)   Mechanical  Drafting. 
(6)    Engineering  Drafting. 

(c)  Agricultural  Drafting.    By  CHARLES  B.  HOWE.    (Ready  shortly.) 

(d)  Architectural  Drafting.     By   CHARLES   B.    HOWE   and  A.    B. 

GREENBERG,  Stuyvesant  Technical  High  School,  New  York. 
(Ready  shortly.) 

(e)  Drafting  for  Plumbers. 
(/)  Drafting  for  Steam  Fitters. 
(g)   Electrical  Drafting. 

(fi)  Drafting  for  Sheet  Metal  Workers  and  Boiler  Makers. 
(i)    Drafting  for  the  Heating  and  Ventilating  Trades. 

APPLIED  MATHEMATICS. 

In  preparation  by  carefully  selected  specialists. 

(a)  Elementary  Applied  Mathematics. 

(b)  Mathematics  for  Machinists. 

(c)  Mathematics  for  the  Woodworking  Trades. 
(of)   Mathematics  for  the  Electrical  Trades. 

(e)    Mathematics  for  the  Metal  Trades. 

THE  LOOSE  LEAF  LABORATORY  MANUAL. 
Ready: 

(a)  Exercises  in  General  Chemistry.   By  CHARLES  M.  ALLEN,  Pratt 

Institute. 

(b)  Exercises  in  Steam;   Strength  of  Materials,  Gas  Engines,  and 

Hydraulics.    By  J.  P.  KOTTCAMP,  Pratt  Institute. 

THE  LOOSE  LEAF  DRAWING  MANUAL.   Reference  and  Problem  Sheets 
to  accompany  the  texts  in  Drafting  and  Design. 


HEAT 


A    MANUAL    FOR    TECHNICAL 
AND    INDUSTRIAL    STUDENTS 


BY 

J.    A.    RANDALL 

Instructor  in  Physics,  School  of  Science  and  Technology,  Pratt  Institute 


FIRST    EDITION 
FIRST   THOUSAND 


NEW  YORK 
JOHN   WILEY   &   SONS 

LONDON:    CHAPMAN  &  HALL,  LIMITED 
1913 


Copyright,  1913 

BY 

J.    A.    RANDALL 


THE    SCIENTIFIC    PRESS 

ROBERT    DRUMMOND    AND    COMPANY 

BROOKLYN,    N.   Y. 


PREFACE 


THIS  text  is  intended  to  set  forth  briefly  the  essential 
principles  of  heat.  The  idea  of  heat  as  a  form  of  molecular 
energy  is  first  made  clear.  The  production,  the  measure- 
ment, the  transmission,  and  the  effects  of  heat  are  then 
discussed.  In  Chapters  V  and  VIII  particular  attention  is 
given  to  a  clear  and  direct  development  of  the  continuity 
of  state,"  and,  in  the  case  of  the  gaseous  state,  to  the  temper- 
ature— pressure — volume — energy  relations  which  have  a 
technical  application.  Care  is  taken  to  make  the  treatment 
progress  slowly  enough  to  make  the  definitions  and  the 
measuring  of  the  physical  constants  clear.  The  matter  is 
developed  with  sufficient  rapidity  and  with  enough  continuity 
to  give  the  reader  a  broad  view  of  the  subject  as  a  whole.  As 
a  further  illustration  of  the  application  of  the  laws  of  heat, 
and  to  give  the  student  a  conception  of  the  use  to  which 
he  should  put  his  study,  in  Chapters  VI,  VII,  and  X,  steam 
power  plants,  gas  power  plants,  and  refrigeration  are  dis- 
cussed. The  attempt  is  made  rather  to  show"  the  function 
of  the  essential  members  and  the  dependence  of  this  func- 
tion upon  the  fund;, mental  laws  of<  heat  energy,  than  to 
give  a  technical  discassion  of  such  plants. 

The  author  has  here  endeavored  to  furnish  the  general 
student  or  reader  with  such  an  insight  into  the  nature  of 
heat  and  its  effects  as  shall  enable  him  to  comprehend, 
reasonably,  the  operation  of  various  power  processes  with 
which  he  may  come  in  contact.  The  book  is  also  intended 


271551 


vi  PREFACE 

to  provide  the  student  who  will  later  take  up  technical 
questions  involving  the  design  and  construction  of  power 
machinery  with  a  background  of  understanding  which  shall 
enable  him  to  more  fully  comprehend  the  problems  with 
which  he  must  deal  and  the  fundamental  heat  considerations 
which  are  involved. 

In  the  treatment  of  the  material,  the  historical  method 
has  been  discarded  as  requiring  too  much  space  as  well  as 
the  introduction  of  material  not  essential  to  a  mastery  of 
the  fundamental  principles.  Heat  as  energy,  and  the 
necessary  processes  and  effects  involved  in  the  production, 
distribution,  and  utilization  of  this  energy  have  been 
selected  as  the  central  themes.  Thus  around  the  energy 
theme  the  mass  of  supplementary  material  is  grouped. 
This  method  of  presentation  has  been  followed  for  several 
years  at  Pratt  Institute  through  the  use  of  a  set  of  mimeo- 
graph sheets  from  which  this  text  has  ultimately  evolved. 
These  sheets  have  also  been  issued  for  the  past  year  in  the 
form  of  a  preprint  and  have  secured  successful  results  at 
Pratt  Institute  and  at  Wentworth  Institute,  Boston,  Mass. 
The  arrangement  and  selection  of  the  material  presented  is 
that  which  has  been  shown  to  be  suitable  by  the  experience 
of  the  teachers  who  have  been  using  these  notes  with  several 
hundred  students  each  year. 

If  any  novelty  may  be  ascribed  to  this  text,  it  is  to  be 
found  in  the  type  of  material  used  as  a  medium  for  the 
presentation  of  the  fundamental  facts  and  laws  of  heat, 
and  in  the  manner  in  which  this  material  is  organized, 
rather  than  in  the  mere  character  of  the  facts  themselves. 
In  this  latter  respect,  no  particular  attempt  at  originality 
has  been  made.  The  language  is  as  simple  as  possible. 
Only  such  technical  words  and  phrases  are  introduced  as 
are  necessary  to  enable  the  student  to  feel  at  home  in  a 
technical  atmosphere,  to  understand  the  current  technical 
literature  of  the  subject,  and  to  handle  reference  books  with 
confidence.  Little  .mathematics  is  required.  A  knowl- 


PREFACE  vil 

edge  of  simple,  algebraic  equations  is  assumed,  and  in 
Chapter  VIII,  logarithms  are  used  in  one  type  of  problem. 

The  numerous,  carefully  selected  problems  constitute 
what  is  believed  to  be  one  of  the  strongest  features  of 
the  book.  These  involve  the  usual  computations  found 
in  elementary  text-books  on  heat.  They  also  include  a 
large  number  of  problems  dealing  with  the  applications 
of  heat  to  common  processes  which  students  observe  daily, 
and  which  involve  fundamental  ideas  of  which  the  student 
ought  to  have  an  intelligent  understanding.  The  number 
and  the  grading  of  these  problems  is  such  that  supple- 
mentary drill  either  in  theoretical  heat  or  in  technical  heat 
may  be  readily  given  by  the  teacher  in  accordance  with 
his  needs. 

Attention  is  called  to  the  general  plan  of  the  text. 
This  is  such  that  the  book  may  be  used  for  either  a  very 
short  course  or  as  a  basis  for  a  long  course  taking  four 
hours  a  week  for  a  semester.  For  a  short  course,  the  fine 
print  should  be  omitted  and  only  Chapters  I  to  V  and  selected 
sections  of  Chapter  XI  should  be  assigned.  Thus,  in  ten 
lessons,  a  general  course  in  theoretical  heat  with  a  brief 
suggestion  of  practical  applications  may  be  given.  A  longer 
course  results  by  assigning  all  of  the  subject-matter,  by 
selecting  problems  which  have  to  do  with  the  processes  and 
principles  involved,  and  by  giving  special  attention  to 
Chapters  VI  to  X.  Thus  the  text  will  furnish,  it  is  believed, 
the  basis  for  a  satisfactory  course  in  heat  for  those  technical 
students  who  are  later  to  go  on  to  the  study  of  the  engineer- 
ing phases  of  the  subject. 

Throughout  the  preparation  of  this  work  the  author 
has  been  aided  by  the  constructive  criticism  suggested  by 
the  experience  of  Mr.  Jameson,  Head  of  the  Department  of 
Physics,  Pratt  Institute,  and  by  his  former  associate,  Mr. 
W.  H.  Timbie,  Head  of  the  Applied  Science  Department, 
Wentworth  Institute,  Boston,  Mass.  Thanks  are  also  due 
to  Prof.  Harvey  N.  Davis,  of  Harvard  University,  to  Prof. 


viii  PREFACE 

H.  H.  Higbie,  of  Wentworth  Institute,  Boston,  Mass.,  and 
to  Mr.  J.  P.  Kottcamp,  of  Pratt  Institute,  for  valued  criti- 
cisms, also  to  Mr.  F.  A.  Clark,  of  Pratt  Institute,  for  proof- 
reading. 

J.  A.  RANDALL. 
BROOKLYN,  N.  Y.,  December,  1912. 


EDITOR'S  NOTE 


THERE  is  at  present  no  American  text  in  Elementary 
Heat  which  emphasizes  the  applications  of  the  fundamental 
principles  of  the  subject  to  the  various  commercial  and 
engineering  processes  in  which  they  are  the  controlling 
factor.  It  is  unfortunate  that  the  student  who  takes  up 
the  study  of  Power  Engineering  should  be  poorly  prepared 
in  the  subject  most  fundamental  to  his  new  undertaking. 
It  is  perhaps  more  unfortunate  that  students  in  elementary 
general  courses  in  Heat  should  fail  to  be  taught  those 
conceptions  which  will  enable  them  to  deal  most  intelli- 
gently with  the  many  problems  in  heating,  ventilation, 
and  the  utilization  of  heat  energy,  which  are  commonly 
encountered  in  the  ordinary  affairs  of  domestic,  business, 
and  industrial  life. 

This  little  text  is  designed  to  meet  the  needs  of  the  above 
two  groups  of  students.  The  author  has  had  long  experi- 
ence in  teaching  Heat  to  classes  of  technical  students.  As  a 
university  student  he  specialized  in  the  subject  upon  which 
he  has  written,  and  since  that  time  he  has  kept  in  close 
contact  with  the  modern  developments  of  Heat  Engineer- 
ing. The  text  will  be  found  to  be  scholarly  and  in  accord- 
ance with  the  terminology  and  usages  of  the  best  modern 
engineering  practice. 

THE  EDITOR. 


IX 


TABLE  OF  CONTENTS 


CHAPTER  I 
ENERGY 

PAGE 

Forms  of  Energy. — Mechanical  Energy. — Chemical  Energy. — 
Electrical  Energy. — Light  Energy. — Heat  Energy,  its  Nature. 
— Kinetic  Theory. — Temperature. — Temperature  Units. — 
Units  of  Quantity  of  Heat  Energy. — Relation  between  Mechan- 
ical Energy  Units,  Heat  Energy  Units,  and  Electrical  Energy 
Units .  1-26 


CHAPTER  II 

ENERGY  FROM  FUELS 

Fuels  and  their  Analysis. — Air  in  Chemical  Reactions. — Energy 
in  all  Chemical  Reactions. — Heat  Energy  of  Fuels. — Explo- 
sives.— Exceptional  Fuels.— Purchasing  Coal. — Heat  Engines. 
—Power  Plant,— Efficiency 27-43 

CHAPTER  III 
SPECIFIC  HEAT  AND  CALORIMETRY 

Specific  Heat. — Specific  Heat  not  a  Constant. — Calorimetry. — 
Method  of  Mixtures. — Water  Equivalent.?— Precautions  in 
Calorimetry.— Other  Methods 44-63 

CHAPTER  IV 
EXPANSION 

Expansion  of  Solids,  Linear. — Coefficient  of  Expansion  of  an 
Area. — Coefficient  of  Cubical  Expansion. — Expansion  of 

xi 


xii  TABLE  OF  CONTENTS 

PAGE 

Liquids. — Expansion  of  Gases. — Boyle's  Law. — Charles'  Law. 
— Pressure  Effects  Due  to  Change  of  Temperature  of 
a  Constant  Volume. — Absolute ,  Temperature. — Expansion 
with  Three  Variables. — Experiments  on  the  Coefficient  of 
Expansion  of  Air. — Expansion  of  Gases. — Boyle's  and  Charles' 
Law  Combined. — Density  and  Volume  Affected  by  Expan- 
sion    64-100 

CHAPTER  V 

THREE  STATES  OF  MATTER 

All  Elements  have  Three  States:  Ice,  Water,  and  Steam. — Latent 
Heat. — Definitions  and  Distinctions. — Dalton's  Law. — Solu- 
tions and  Mixtures. — Distillation. — Cooling  Towers. — Analy- 
sis of  Latent  Heat  of  Vaporization. — Relation  between  the 
Pressure  and  the  Temperature  of  Steam. — Experimental 
Determination  of  this  Relation. — Steam  Tables. — Superheated 
Steam 101-138 

CHAPTER  VI 

FUNCTION  OF  A  STEAM  POWER  PLANT 

A  Simple  Plant. — Effective  Pressure. — Circulation  of  Water, 
Flue  Gases,  etc. — Energy  Circulation. — Computation  of 
Power. — Energy  Utilization. — Steam  Boiler. — Efficiency  of 
the  Boiler. — Water  Rate. — Feed-water  Heaters  and  Econo- 
mizers— Condensers. — Steam  Engine  Functions. — Rankine 
Cycle 139-177 

CHAPTER  VII 
FUNCTION  OF  A  GAS  POWER?PLANT 

Comparative  Efficiency. — Fuels. — Carbureter. — Vaporizer. — Firing 
Systems. — Cycles. — Fuel  Circulation  in  a  Producer  Gas  Power 
Plant.: — Energy  Circulation. — Explosive  Mixtures. — Work- 
ing Medium 178-197 


TABLE  OF  CONTENTS  xiii 

CHAPTER  VIII 
EXPANSION  OF  GASES — Continued 

PAGE 

Specific  Heat  of  a  Gas:  At  Constant  Volume;  at  Constant 
Pressure. — Isothermal  Expansion. — Adiabatic  Expansion. — 
Quantity  of  Energy  in  Gases. — Reversible  Processes. — 
Entropy 198-222 

CHAPTER  IX 

CONVECTION,    CONDUCTION,    RADIATION,    AND    THE    INSULATION   OF 

BODIES 

Convection  of  Heat  Energy. — The  Draft  of  a  Chimney — Con- 
duction of  Heat  Energy. — Units  and  Computation  of  Con- 
ductance.— Insulation. — Radiation  Laws. — Black  Body  Radia- 
tions.— Relation  of  Visible  Radiations  to  Heat  Radiations. — 
Insulating  Devices 223-245 

CHAPTER  X 
FUNCTION  OF  THE  REFRIGERATOR  PLANT 

Household  Refrigeration. — Mechanical  Refrigeration. — Energy 
Flow  through  a  Compression  Type  Plant. — The  Steam  Cycle 
and  the  Ammonia  Cycle  Compared. — Computations. — The 
Absorption  Plant. — Cryogens. — Mechanical  Production  of 
Low  Temperatures. — Insulation  of  Cold  Storage  Spaces . ,  246-267 

CHAPTER  XI       . 

INSTRUMENTS 

Instruments  for  the  Measurement  of  Temperature. — Mercury 
Thermometers,  their  Manufacture,  and  Purchase. — Con- 
struction of  Mercury  Thermometers. — Alcohol  Thermome- 
ters.— Differential  Thermometers. — Gas  Thermometers. — 
Pyrometers. — The  Bolometer. — Thermo-j unction  Pyrometers. 
—Heat  Radiation  Pyrometers. — Optical  Pyrometers. — Fuel 
Calorimeters.— Steam  Indicators .  .  268-294 


xiv  TABLE  OF  CONTENTS 

APPENDIX  A 
TABLES 

PAGE 

Useful  Numbers. — Relation  between  Units. — Heat  Energy  Devel- 
oped by  Oxidation. — Analysis  of  Various  Coals. — Gas 
Analyses. — Specific  Heat. — Coefficient  of  Expansion. — Melt- 
ing-points, Boiling-points,  and  Latent  Heats. — Steam  Tables. 
— Pressure-Entropy  Tables. — Specific  Heat  of  Superheated 
Steam.— Wave  Lengths  of  Various  Waves. — Temperatures  of 
Hot  Bodies.— Conductances 295-307 

APPENDIX  B 
Barometer  Corrections 308-309 

APPENDIX  C 
Significant  Figures 310-313 

APPENDIX  D 
Curves 314-321 

APPENDIX  E 

Extracts  from  A.S.M.E.  Power  Test  Preliminary  Report  .  . .   322-325 
INDEX.  .  327-331 


HEAT 


CHAPTER   I 
ENERGY 

THE  utility  of  any  bit  of  human  knowledge,  taken  by 
itself,  is  not  great.  The  full  significance  is  not  realized 
until  we  get  a  clear  understanding  of  the  relation  of  one 
fact  to  all  others.  Then  only  can  we  apply  knowledge  to 
maximum  advantage. 

While  everyone  knows  much  about  "Heat,"  the  relation 
that  this  information  bears  to  other  knowledge,  which  we 
classify  under  mechanics,  electricity,  and  other  applied 
subjects,  is  established  more  clearly  in  the  mind  by  a  proc- 
ess of  systematization  and  correlation. 

The  most  helpful  topic  under  which  to  correlate  the 
facts,  principles  and  laws  which  are  usually  studied  in  applied 
physics  is  energy. 

1.  Energy.  If  we  are  scientifically  exact,  we  find  that 
there  are  many  conceptions  of  elementary  things,  like 
electricity,  matter  and  energy,  which  cannot  be  exactly 
defined.  Yet  energy  is  such  a  common  and  well-known 
thing  that  we  all  think  we  know,  well  enough  for  all  prac- 
tical purposes,  what  it  is.  For  a  rough-and-ready  sort  of 
definition  we  say  that  "  Energy  is  what  makes  things  go." 
This  is  naturally  our  first  idea  of  energy,  because  we  are 
made  conscious  of  the  existence  of  energy  by  active 
processes. 


2  ,    .  /.    .  HEAT 

We  must  recognize  that  the  energy  exists  all  the  while, 
even  though  it  attracts"  no'  attention  to  itself.  Thus  in 
a  shell  loaded  with  powder  we  have  a  quantity  of  energy 
stored  in  the  powder.  When  we  explode  the  shell  the  energy 
is  largely  transferred  to  the  bullet.  When  the  bullet  hits 
another  body  the  energy  is  partly  passed  on.  If  we  never 
heard  about  burning  powder  and  being  hit  by  bullets,  we 
would  know  nothing  about  the  energy  in  a  cartridge. 
Though  the  cartridge  is  never  exploded  and  we  never 
suspect  the  energy  within,  clearly  it  exists  there  just 
the  same.  Accordingly  a  full  investigation  of  energy 
should  concern  itself  with  energy  when  it  is  passive,  as 
well  as  when  an  active  transfer  is  taking  place. 

Sections  2  and  3  will  be  devoted  to  a  discussion  of 
"ENERGY  OF  MOTION,"  and  "FIXED  ENERGY"  under  which 
headings  all  forms  of  energy  may  be  classified. 

When  the  cartridge  previously  referred  to  is  exploded, 
energy  is  transferred  from  the  explosive  to  the  projectile, 
and  we  say  that  work  is  done  upon  the  projectile.  In 
practically  all  cases  where  work  is  done  a  careful  analysis 
of  the  process  will  show  that  energy  has  been  transferred. 
This  leads  us  to  define  work  as  the  quantity  of  energy 
transferred. 

If  we  make  a  quantitative  study  of  energy,  we  use  one  of 
the  work  units  given  in  Table  II  to  express  quantity  of  energy. 

From  our  knowledge  of  mechanics  we  recall  that  work  is  done 
when  a  force  is  applied  to  a  body  and  the  body  moves  while  the  force 
is  still  acting.  Thus,  if  a  force  of  1  Ib.  is  exerted  through  a  distance 
of  1  ft.,  1  ft.-lb.  of  work  is  done.  If  the  1  Ib.  is  applied  through  2  ft., 
then  2  ft.-lbs.  of  work  are  done.  Similarly,  if  a  2  Ib.  force  presses  against 
a  body  and  it  moves  in  the  direction  of  pressure  1  ft.,  2  ft.-lbs.  of 
work  will  again  be  done.  Work,  therefore,  is  measured  by  the  product 
of  the  two  factors — force  and  distance, 

Work  =  force  Xdistance. 

Whenever  we  say  that  a  body  possesses  energy,  we 
mean  that  it  is  capable  of  doing  work.  If  we  use  all 


I.     ENERGY  3 

the  energy  to  do  work,  and  if  we  lose  none  in  the 
process,  the  quantity  of  work  done  is,  by  our  definition, 
an  exact  measure  of  the  quantity  of  energy  present.  Thus, 
suppose  we  have  a  coiled  spring,  and  we  use  it  to  lift  a 
weight.  If  we  find  that  the  spring  is  able  to  do  50 
ft.-lbs.  of  work,  we  say  that  it  contains  50  ft.-lbs. 
of  energy. 

The  converse  of  this  proposition  is  also  true.  There 
can  be  no  work  done  unless  energy  is  taken  from  some 
body.  The  amount  of  energy  so  taken  must  be  at  least 
equal  to  the  amount  of  work  done. 

2.  Energy  of  Motion.  All  bodies,  that  are  in  motion, 
however  large  or  small  they  may  be,  are  said  to  possess 
energy  of  motion,  or  "KINETIC  ENERGY."  If  a  body,  as  the 
head  of  a  hammer  is  in  motion,  it  is  capable  of  doing  work 
because  of  that  motion.  The  amount  of  work  that  this 
body  is  able  to  do  is  measured  by  the  product  of  force 
the  hammer  can  exert  upon  another  body  times  the  distance 
through  which  this  force  is  exerted.  A  demonstration  of 
the  following  may  be  found  in  any  book  on  mechanics. 

WV2 
Kinetic  energy,   or  KE,  —FD——^ — , 

where  F  is  the  force,  D  is  distance  through  which  the  force 
acts,  W  is  the  weight  of  moving  body,  V  its  velocity,  and 
g  is  acceleration  due  to  gravity  in  the  same  system  of  units 
as  W. 

Thus  if  we  find  that  the  hammer  has  driven  a  nail 
\  in.  against  an  average  resistance  of  216  Ibs.,  there  was 
iX  iVX216  or  9  ft.-lbs.  of  work  done,  and  therefore  9  ft.-lbs. 
of  energy  were  in  the  hammer.  Or  if  it  is  determined  that 
the  velocity  of  the  hammer  just  as  it  hits  the  nail  is  24 
ft. /sec.,  and  the  weight  of  the  hammer  head  is  1  lb.,  then 
the  kinetic  energy  is 

1X24X24  ... 
-2X32-  ft"lbs" 


4  HEAT 

which  equals  9  ft.-lbs.  again,  and  is  a  true  measure  of  the 
work  the  hammer  can  do,  and  therefore  of  its  energy. 

Steam  engines,  motors,  generators,  water  turbines,  etc., 
furnish  a  fairly  steady  stream  of  energy  of  motion  to 
machinery  connected  with  them.  The  amount  of  energy 
furnished  is  always  measured  by  determining  the  work 
done. 

Other  illustrations  of  energy  of  motion  are  discussed 
under  "  Electrical  Energy,"  and  "  Light  Energy."  See 
Sections  7  and  8. 

3.  Fixed  Energy.  The  continuous  supply  of  energy  of 
motion  delivered  by  a  steam  engine  is  drawn  from  the 
coal,  wood,  or  oil  burned  under  a  boiler.  This  coal  is  said 
to  contain  FIXED  ENERGY,  since  the  coal  and  its  contained 
supply  of  energy  may  be  kept  indefinitely  without  appre- 
ciable loss. 

Sometimes  we  speak  of  kinetic  energy  or  energy  of  motion  as 
being  stored  in  a  fly-wheel,  but  it  will  be  noticed  that  this  is  but 
temporary,  since  the  energy  of  motion  of  a  fly-wheel  or  other  piece 
of  machinery  soon  leaks  away  if  not  put  to  prompt  use.  Clearly 
this  is  not  fixed  energy. 

Coal  is  only  one  of  a  large  number  of  substances  which 
tend  to  oxidize  or  burn  and  in  so  doing  free  energy.  In 
general,  fixed  energy  is  stored  in  all  chemicals  that  are 
mutually  eager  to  unite,  or  that,  because  of  an  unstable 
internal  arrangement  of  the  small  particles  that  go  to 
make  up  the  mass,  are  eager  to  readjust  themselves. 

In  mechanics,  we  have  a  kind  of  "  fixed  energy  "  which 
is  often  called  "  potential  energy,"  or  "  energy  of  position." 
Thus,  if  a  weight  is  raised  to  a  height  above  the  earth, 
it  has  energy  due  to  its -height,  and  if  it  is  allowed  to  fall 
it  will  gradually  transform  its  energy  of  position,  or  stored 
or  fixed  energy,  into  energy  of  motion  or  kinetic  energy. 
This  transformation  will  be  complete  at  the  instant  when  the 
weight  hits  the  ground.  We  will  see  presently  that  when  the 


I.     ENERGY  5 

weight  hits  the  ground  the  energy  is  not  lost,  but  passes 
on  to  other  bodies. 

Other  common  illustrations  of  potential  energy  are: 
water  elevated  to  a  reservoir  or  tank,  a  coiled  spring  held 
by  a  detent,  and  any  elastic  body  held  out  of  its  normal  shape. 

4.  Forms  Classified.  In  the  table  below  are  shown  the 
forms  that  energy  of  motion  and  fixed  energy  take. 


Energy  of  Motion. 

Fixed  Energy. 

a. 

Mechanical  energy 

a.  Mechanical  energy 

b. 

Electrical  energy 

b.  Electrical  energy 

c. 

Light  energy 

d. 

Heat  energy 

e.  Chemical  energy 

5.  Mechanical  Energy.     Energy  possessed  by  a  mass  as 
a  whole  is  called  "  mechanical  energy."     If  the  energy  of 
a  body  is  considered  to  be  due  to  the  motion  of  the  body 
as  a  whole,  the  energy  is  said  to  be  "  kinetic  energy  in  the 
mechanical  form." 

If  the  energy  of  a  mass  is  due  to  its  position,  or  if  the 
energy  contained  in  a  mass  is  due  to  its  elasticity,  the 
energy  is  said  to  be  "  potential  energy  in  the  mechanical 
form." 

These  terms  are  doubtless  thoroughly  familiar,  but,  if 
a  full  discussion  is  desired,  consult  any  mechanics  text-book 
or  encyclopedia. 

6.  Chemical   Energy.     Every    chemical    reaction    that 
takes  place  is   accompanied  by  the"  giving  or  taking  of 
energy  hi  quantities  definitely  proportioned   to  the  weight 
of  the  chemicals  involved.     The  case  of  the  oxidation  of 
coal,  oil,  wood,  etc.,  has  already  been  referred  to.     It  is 
familiar  because  of  the  daily  use  of  these  substances  to  supply 
large  quantities  of  energy.     Most  metals  also  are  oxidized 
with  an  accompanying  emission  of  heat.     Zinc  mill  explosions 
have  occurred  due  to  the  sudden  oxidation  of  floating  particles 


6  HEAT 

of  zinc  in  the  air.  It  is  very  interesting  to  see  a  red-hot 
steel  wire  thrust  into  liquid  oxygen  at  abtfut  —182°  C. 
The  burning  of  the  steel  liberates  enough  heat  to  warm  up 
the  oxygen  from  its  very  low  temperature  to  that  of  white- 
hot  steel  and  in  addition  to  maintain  the  wire  at  a  white 
heat  in  its  cold  bath. 

No  less  interesting  is  the  way  chemical  energy  is  stored 
and  given  off  in  various  kinds  of  electrical  batteries.  In 
the  type  called  primary  batteries  the  chemical  energy  is 
transformed  into  electrical  energy,  and  when  the  supply 
of  energy  is  exhausted  new  chemicals  are  installed.  In 
the  so-called  secondary  batteries  advantage  is  taken  of  the 
fact  that  the  chemical  reactions  are  reversible.  When  the 
supply  of  energy  in  a  secondary  battery  has  been  nearly 
exhausted,  electrical  energy  is  sent  into  it,  the  chemical 
reaction  is  reversed,  and  a  new  supply  of  chemical  energy 
stored  up.  The  propriety  of  the  name  "  storage  battery  " 
for  the  chemical  secondary  battery  is  apparent. 

Chemical  energy  is  fixed  or  stored  energy  due  to  the  desire 
of  one  chemical  substance  to  unite  with  another. 

7.  Electrical  Energy.  Wherever  a  quantity  of  elec- 
tricity exists  energy  is  present  in  the  "  electrical  form." 
The  electricity  does  work  only  when  it  is  flowing,  so  we  are 
mainly  interested  in  electric  current.  The  work  done  by 
an  electric  current  is  computed  by  finding  the  product  of 
the  current X pressure  X time.  The  usual  practical  unit  of 
work  is  the  kilowatt-hour,  which  equals  amperes  X  volts 
Xtime  in  hours  divided  by  1000. 

The  introduction  of  time  into  this  computation  is  a  frequent 
cause  of  misunderstanding  of  the  true  nature  of  work  and  energy. 
Amperes  X  volts  is  really  a  rate  of  doing  work,  since  amperes  is  really 

rate  of  flow  and  is  expressed  by  the  rate:  .     In  the  power 

time 

quantity  X  pressure 

unit  then,  we  have  ; — — ,  and  to  get  our  work  in  any 

time 

practical  case  we  must  multiply  by  the    time  during  which  power 


I.     ENERGY  7 

was  being  delivered  at  the  rate  indicated  by  the  above  expression, 
and  we  get 

quantity  X  pressure  Xtime 
time 

which  equals  quantity  X  pressure  when  the  time  has  been  canceled. 
Thus  it  will  be  seen  that  work  and  energy  are  measured  electrically 
by  taking  the  product  of  the  quantity  of  flow  times  the  pressure. 

Commercially,  electrical  energy  is  transformed  in  large 
quantities  by  generators  from  mechanical  energy  delivered 
by  either  steam  engines,  water  turbines,  or  explosion  engines. 
This  energy  flows  in  streams  through  the  electrical  circuit 
just  as  kinetic  energy  flows  in  streams  from  the  steam  engine 
or  through  any  machines  connected  to  it.  Therefore  we 
class  electrical  energy  as  energy  of  motion,  although  there 
is  one  piece  of  apparatus,  the  condenser,  in  which  it  can 
be  fixed  for  short  intervals  of  time.  For  a  full  discussion 
of  electrical  energy,  see  any  electrical  text-book  or  ency- 
clopedia. 

8.  Light  Energy.  There  is  a  fairly  well  substantiated 
theory  that  all  bodies  are  giving  off  a  wave  form  of  motion. 
Since  no  o'ne  has  been  able  to  find  that  these  waves  depend 
upon  any  form  of  matter  for  their  propagation,  it  has  been 
assumed  that  they  are  wave  disturbances  in  an  unknown 
medium  called  "  luminiferous  ether/'  which  is  supposed 
to  uniformly  pervade  all  space.  When  these  ether  waves 
are  thrown  from  fairly  hot  bodies  some  of  them  affect  the 
human  eye  and  are  called  light  waves,  or  rays  of  light. 
These  rays  of  light  that  affect  the  eye  are  only  part  of  the 
waves  that  are  given  off,  as  the  eye  recognizes  waves 
only  within  a  limited  range  of  wave  lengths.  The  longer 
wave  lengths,  however,  we  can  feel  when  dense  rays  fall 
on  our  skin.  These  are  the  rays  that  we  feel  when  we 
are  at  some  distance  from  a  hot  stove  or  a  bonfire. 
Such  rays  are  called  "  heat  rays."  The  shorter  wave 
lengths  usually  come  from  extremely  hot  bodies  and  have 


8  HEAT 

a  strong  disintegrating  effect  upon  many  substances. 
These  are  called  "  ultra-violet  rays." 

The  only  income  of  energy  that  the  earth  has  is  received 
in  the  form  of  these  radiations  from  the  sun  and  other 
heavenly  bodies.  But  the  earth  is  also  giving  off  large 
quantities  of  energy  in  this  form  although  the  earth  is  so 
cool  that  the  length  of  its  waves  is  too  great  to  affect  our 
eyes  and  not  so  numerous  as  to  affect  our  senses. 

If  we  try  to  balance  the  earth's  energy  account,  every- 
thing points  to  a  continuous  loss  of  energy  by  the  earth. 

The  energy  of  the  sun's  rays  is  put  to  use  in  plants 
to  build  up  from  elements  and  extremely  simple  compounds 
the  complex  chemical  compounds  of  which  they  consist. 

Because  of  these  well-known  facts,  "  light  "is  an 
extremely  familiar  form  of  energy.  As  it  has  velocity  of 
about  192,000  miles  a  second,  it  clearly  must  be  classed 
as  energy  of  motion. 

9.  Heat  Energy:  Its  Nature.  When  light  energy  falls 
upon  a  body  and  is  absorbed,  we  notice  that  the  body 
becomes  "  warmer." 

Now  we  know  that  there  is  energy  in  the  light  rays 
but  apparently  the  wave  motion  is  destroyed  when  the 
waves  come  in  contact  with  the  body;  consequently  the  energy 
no  longer  exists  as  light  energy.  It  would  seem  as  if  this 
giving  up  of  energy  has  something  to  do  with  the  body 
getting  "  warmer." 

Again,  if  we  send  an  electric  current  through  this  body, 
we  shall  find  that  it  takes  energy  to  do  so  and  that  the 
body  is  again  made  "  warmer."  Here  electrical  energy 
apparently  warms  the  body. 

Likewise,  if  we  rotate  a  shaft  in  a  bearing,  we  find  that 
it  takes  energy  to  keep  it  rotating,  and  that  the  bearing 
tends  to  become  "  warmer."  In  this  case  we  notice  that 
just  where  our  mechanical  energy  disappears  we  get  certain 
effects,  which  we  describe  by  saying  that  the  body  has 
become  "  warmer." 


I.     ENERGY  9 

It  would  appear  that  in  these  cases  energy  in  various 
forms  has  been  used  upon  the  body  with  the  result  that 
in  each  case  the  body  has  become  "  warmer." 

Consider  the  case  in  which  a  mass  is  repeatedly  struck 
with  a  hammer:  The  mechanical  energy  in  the  hammer  is 
given  up  and  no  longer  exists  as  mechanical  energy  of  motion 
of  the  mass.  Clearly  it  is  either  lost  or  is  in  the  mass  and  in 
the  hammer.  If  we  place  a  therm oj unction  against  the 
mass  before  striking  it  and  if  the  mass  is  at  the  same 
temperature  as  the  thermo junction,  no  electric  current 
will  flow  through  a  connected  galvanometer.  If,  how- 
ever, the  junction  is  taken  away,  the  mass  repeatedly 
struck  with  the  hammer,  and  the  junction  again  placed 
adjacent  to  the  warmed  mass,  the  junction  will  draw  some 
warmth  from  the  mass  and  we  will  notice  a  deflection  of 
our  galvanometer.  We  shall  then  have  ELECTRICAL  ENERGY 
in  our  circuit,  which  we  have  drawn  from  the  mass,  causing 
a  loss  of  warmth.  Since  we  have  transformed  mechanical 
energy  into  heat,  and  then  transformed  heat  back  into 
electrical  energy,  it  would  appear  from  this  that  heat  is 
a  form  of  energy  since  from  the  heat  work  was  done. 

Consider  the  case  of  a  gasoline  engine. 

Air  and  gasoline  are  mixed  in  a  carbureter  and  sucked 
into  a  cylinder  in  the  gaseous  form.  By  a  spark  or  other 
means  the  gasoline  is  burned  quickly,  or  as  we  say,  exploded, 
and  great  heat  is  generated.  This  heat  tends  to  expand 
the  gas  and  produces  a  high  pressure.  The  pressure  forces 
the  piston  out  and  work  is  done.  The  energy  now  is  in 
the  mechanical  form  and  the  piston  passes  part  of  it  on 
to  some  other  machine  or  to  the  fly-wheel,  where  it  may 
be  temporarily  stored. 

While  the  engine  goes  through  this  series  of  operations, 
it  takes  in  energy  in  the  chemical  form,  and  by  first  chang- 
ing this  energy  into  heat,  delivers  energy  in  the  mechanical 
form.  (See  the  definition  of  "engine,"  p.  37.)  In  this 


10 


HEAT 


example  heat  again  seems  to  be  a  form  of  energy,  for  from 
the  heat  work  was  done. 

If  a  weight  is  allowed  to  fall  from  a  height  and  give  up 
energy  to  a  quantity  of  water  by  stirring  it  as  is  done  in 
the  apparatus  shown  in  Fig.  1,  after  the  water  comes  to 
rest  it  will  be  warmer.  In  other  words,  the  mechanical 
energy  of  the  weight  has  been  transferred  into  heat  energy 
of  the  water. 


FIG.  1. — Joule's  Mechanical  Equivalent  Apparatus. 

The  mechanical  energy  was  derived  from  the  motion 
of  a  mass.  The  heat  energy  is  present  without  any  motion 
of  the  mass  of  water,  but  seems  to  be  internal. 

The  accepted  conception  of  the  nature  of  heat  energy 
is  the  "  kinetic  theory,"  which,  briefly  stated,  is  that  heat 
energy  is  due  to  the  motion  of  the  small  particles — molecules 
— which  go  to  make  up  a  mass. 

The  prevailing  scientific  conception  of  matter  is  that  a  mass  is 
made  up  of  molecules.  These  molecules  in  turn  are  made  up  of  atoms, 
of  which  there  are  about  81  kinds  known.  The  atom  is  not  now 
considered  to  be  the  smallest  division  of  matter,  but  is  supposed  by 


I.     ENERGY  11 

some  scientists  to  be  made  up  of  a  varying  number  of  electrons  plus 
a  corpuscle.  A  notion  of  the  relative  size  of  a  mass,  molecule,  and 
atom  may  be  had  by  considering,  first,  a  crystal  mass  of  cane-sugar. 
This  is  made  up  of  a  large  number  of  molecules,  each  in  turn  containing 
not  less  than  45  atoms  .of  various  kinds.  In  a  similar  way  we  have 
the  universe,  made  up  of  solar  systems,  of  which  our  sun  and  the 
bright  stars  are  centers.  These  solar  systems  are  made  up  of  a  sun 
and  a  number  of  planets.  The  ratio  between  the  diameter  of  the  solar 
system  and  the  diameter  of  the  universe  we  conceive  as  a  very  small 
fraction.  Also  the  ratio  between  the  diameter  of  the  solar  system  and 
one  of  the  planets  is  a  very  small  fraction.  Of  the  same  order 
of  magnitude  as  the  first  fraction  is  the  concept  of  the  ratio  between 
the  diameter  of  the  mass  and  the  diameter  of  a  sugar  molecule. 
Similarly,  the  ratio  between  the  diameter  of  an  atom  and  a  molecule 
is  thought  of  as  in  proportion  to  the  ratio  of  the  diameter  of  the  earth 
and  our  solar  system. 

According  to  the  kinetic  theory,  we  must  think  of  the 
molecules  that  go  to  make  up  a  mass  as  in  constant  motion. 
The  orbit  of  this  motion  is  extremely  small  relatively  to 
the  whole  mass,  yet  extremely  large  relatively  to  the 
diameter  of  the  molecule.  The  orbit  of  this  motion  is 
restricted  by  occasional  collisions  which  probably  take 
place  between  only  two  molecules  at  a  time  as  the  molecules 
are  so  sparsely  scattered  in  the  mass. 

The  energy  of  the  molecule  due  to  its  motion  will  be 

WV2 
measured  by  the  usual  formula,  KE  =  -^—.    For  a  fixed 

weight  of  any  given  substance  and  consequently  for  each 
molecule,  we  find  that  the  heat  energy  is  approximately 
in  proportion  to  its  temperature.  But  since  heat  energy 
is  due  merely  to  the  kinetic  energy  of  the  molecule,  the 
mean  velocity  of  the  average  molecule  must  vary  as  the 
square  root  of  the  temperature,  or  this  velocity  squared 
must  vary  as  the  temperature  varies. 

An  interesting  experiment  is  sometimes  made  to  suggest  the  way 
the  stored  energy  of  a  whole  mass  when  it  falls  and  acquires  kinetic 
energy  suddenly  is  transformed  to  heat  energy  when  it  strikes  another 
body.  Notice  what  happens  when  a  drop  of  mercury  falls  from  a 


12 


HEAT 


C.      F. 


height.  It  first  has  potential  energy  due  to  its  position,  which  is 
changed  to  kinetic  energy  just  before  it  reaches  the  floor.  When  it 
strikes  the  floor  the  motion  of  the  mass  stops,  but  a  large  number  of 
small  globules  of  mercury  scatter  in  every  direction  at  a  rapid  rate. 
If  instead  of  allowing  the  mercury  to  fall  upon  the  floor,  it  be  made  to 
fall  into  a  closed  vessel  and  if  the  temperature  be 
determined  before  the  mercury  falls  and  again  after 
it  is  collected  in  the  vessel,  the  mercury  will  be  found 
warmer  after  the  experiment.  Clearly,  in  this  event, 
the  potential  energy  of  the  mercury  due  to  its 
position  is  changed  to  heat  energy,  and  the  energy 
has  been  transferred  to  the  molecules. 


10.  Temperature      and      Temperature 

Units.  Whenever  we  increase  the  amount 
of  heat  energy  stored  in  a  body,  as  when 
we  strike  it  with  a  hammer,  we  can  feel  an 
effect  that  we  describe  by  saying  that  the 
body  is  warmer.  When  we  take  away  heat 
we  say  that  the  body  is  cooler.  Thus 
temperature  is  always  relative  to  a  pre- 
vious condition,  or  relative  to  some  fixed 
condition  which  we  have  in  mind,  and 
expresses  how  much  warmer  or  cooler  a 
body  is  relatively  to  a  standard  condition. 


C.     F. 


We  use  the  words  hot  and  cold  to  indicate  direc- 
tion in  which  energy  may  be  expected  to  be  trans- 
ferred. Hot  and  cold  do  not  indicate  the  state 
or  temperature  of  a  body. 

As  a  standard  to  which  to  refer  differ- 
ences of  temperature,  the  civilized  world 
has  agreed  upon  the  freezing- and  boiling- 
points  of  pure  water  under  a  pressure  of 
760  mm.  of  mercury.  In  order  to  express 
more  definitely  the  amount  hotter  or  colder,  the  differ- 
ence in  temperature  between  these  two  fixed  points  of 
reference  has  been  divided  into  an  arbitrary  number  of 
divisions  called  degrees.  The  number  of  degrees  between 


FIG.  2. 


I.     ENERGY 


13 


the  freezing-point  and  the  boiling-point  of  water  in  the 
English  or  Fahrenheit  scale  is  180;  and  in  the  French  or 
Centigrade  is  100. 

In  daily  conversation  people  frequently  express  tem- 
perature by  saying  that  it  is  so  many  degrees  Fahrenheit 
of  centigrade  above  freezing,  which  is  the  logical  beginning 
of  a  temperature  scale  for  daily  use.  In  the  centigrade 
system  freezing  is  the  zero  point.  About  the  year  1714, 
Fahrenheit,  one  of  the  first  to  undertake  accurate  temper- 
ature measurements,  selected  the  lowest  point  that  he  could 
reach  by  artificial  means  as  the  zero  of  his  scale,  and  the 
temperature  of  the  human  body  as  100°.  In  the  scientific 
evolution  of  his  thermometer,  the  scale  was  slightly  altered 
to  use  the  freezing-  and  boiling-points  of  water  as  points  of 
reference.  When  freezing  was  taken  as  32°,  and  boiling 
212°,  blood  heat  turned  out  to  be  98°.  It  thus  happens 
that  the  thermometer  most  used  by  English-speaking  people 
has  a  very  illogical  and  awkward  scale. 

These  facts  about  the  various  temperature  scales  are 
shown  in  the  table  below,  and  in  the  diagrams  appended. 

A  further  discussion  of  thermometers  will  be  found  in 
Chapter  VII. 


Abbre- 
viation. 

Freezing- 
point 
Number. 

Boiling- 
point 
Number. 

Difference 
between 
Fixed  Points. 

Centigrade  

C. 

0° 

100° 

100 

Fahrenheit 

F. 

32° 

212° 

180 

•"  j 

To  change  from  one  scale  to  another  these  facts  should 
be  kept  in  mind: 

(a)  The  difference  in  zero  point; 
(6)  The  difference  in  value  of  one  degree  on  the  scale. 
100  centigrade  degrees  =  180  Fahrenheit  degrees. 


14  HEAT 

1  centigrade  degree  =  f  Fahrenheit  degree. 

§  centigrade  degree  =  1  Fahrenheit  degree. 

To  change  a  centigrade  temperature  to  the  correspond- 
ing Fahrenheit  temperature,  it  is  necessary  to  multiply  by 
nine-fifths  to  find  the  number  of  degrees  Fahrenheit  above 
the  freezing-point  and  then  add  32°. 

To  change  a  Fahrenheit  temperature  to  the  corresponding 
centigrade  temperature,  it  is  first  necessary  to  subtract 
32°,  and  then  multiply  by  five-ninths. 

Problem  1.    Change  95°  F.  to  C. 

95°  F.  is  63  Fahrenheit  degrees  above  the  freezing-point. 
1  F.  degree  =f  of  1  C.  degree,  thus  63°  F.=63x|  or  35 

C.  degrees. 

35  C.  degrees +0  (value  of  freezing-point)  =35°  C. 
or        95°F.=35°C. 

Problem  2.     Change  40°  C.  to  F. 

40°  C.  is  40  centigrade  degrees  above  freezing-point. 

1  C.  degree  =|  of  1  F.  degree,  thus  40  C.  degrees  =40  x£  =72 

F.  degrees. 

72  F.  degrees  +32°  (value  of  freezing-point)  =  104°  F. 
or        40°C.=104°F. 

Problem  3.    Change  50°  C.  to  F. 
Problem  4.    Change  240°  F.  to  C. 
Problem  5.     Change  -40°  C.  to  F. 
Problem  6.    Change  -20°  F.  to  C. 

Problem  7.  If  the  temperature  of  your  body  is  98°  F.,  what 
would  it  be  in  centigrade? 

Problems.  Zinc  melts  at  approximately  415°  C.;  what  is 
its  melting-point  on  the  Fahrenheit  scale? 

Problem  9.  If  oxygen  boils  at  -297°  F.,  what  is  its  boiling- 
point  on  the  centigrade  scale? 

Problem  10.  If  carbon  dioxide  boils  at  —  79°  C.,  what  is  its 
boiling-point  on  the  Fahrenheit  scale? 

11.  Units  of  Quantity  of  Heat  Energy.  It  would  natu- 
rally be  expected  from  our  previous  discussion  of  energy 
that  the  logical  unit  by  which  to  measure  heat  energy  is 
a  work  unit.  However,  no  convenient  work  unit  is  avail- 
able, and  we  must  use  units  which  have  in  them  as  factors 
temperature  and  quantity  of  mass. 


I.     ENERGY  15 

For  experimental  purposes  the  most  convenient  material 
for  a  standard  mass  is  water,  as  it  is  easily  obtainable  in  a 
chemically  pure  state,  and  has  a  very  great  heat  capacity 
per  unit  of  weight.  Accordingly,  in  the  metric  system  we 
have  as  our  unit  of  heat  quantity  the  calorie. 

A  Calorie  is  THE  AMOUNT  OF  HEAT  ENERGY  NECES- 
SARY TO  CAUSE  ONE  GRAM  (1  c.c.)  OF  PURE  WATER  TO 
RISE  1°  C. 

The  corresponding  English  unit  is  the  British  thermal 
unit. 

A  British  Thermal  Unit  (B.T.U.)  is  THE  AMOUNT  OF 
HEAT  ENERGY  NECESSARY  TO  CAUSE  A  POUND  OF  PURE 
WATER  TO  RISE  1°  F. 

1  B.T.U.  =  252  calories. 

Other  units  are  useful  at  tunes  when  the  B.T.U.  or  the 
calorie  is  too  small  or  when  using  a  thermometer  system 
different  from  the  weight  system.  Although  not  in  common 
use  for  permanently  recording  experimental  results,  in 
computations  and  in  taking  data  the  following  correctly 
represent  a  definite  amount  of  heat  energy,  and  may  be 
used  in  exactly  the  same  way  as  the  calorie  and  the  B.T.U.: 

1  Ib. -degree  C., 
1  ton  -degree  C., 
1  ton  -degree  F., 
1  kgr .-degree  F., 
1  kgr  .-degree  C,  etc.. 

These  units  of  quantity  of  heat  energy  should  be  care- 
fully distinguished  from  units  of  temperature.  Temper- 
ature alone  tells  us  nothing  about  the  quantity  of  heat 
energy  in  a  body,  but  merely  whether  we  may  expect 
heat  energy  to  be  transmitted  to  or  from  other  neighboring 
bodies  whose  temperature  is  also  known.  The  quantity 
unit  is  a  measure  of  the  amount  of  energy  so  transmitted. 

For  work  demanding  accuracy  exceeding  one  part  in  500,  the 
quantity  unit  should  be  more  exactly  denned.  The  inaccuracy  arises 


16  HEAT 

from  the  fact  that  the  quantity  of  heat  energy  necessary  to  raise  a 
given  mass  of  water  1  is  not  constant.  In  fact,  below  the  boiling- 
point  there  is  a  maximum  variation  of  nearly  one  per  cent.  How- 
ever, if  experiments  are  always  conducted  with  the  water  below  50° 
C.,  an  error  exceeding  •£-  per  cent  is  not  probable. 

There  is  a  strong  tendency  to  take  as  the  more  accurate  definition 
of  the  calorie  the  energy  necessary  to  heat  1  gr.  from  19.5°  C.  to  20.5°  C. 
and  for  the  B.T.U.  the  energy  to  heat  1  Ib.  from  67°  F.  to  68°  F.  Some 
scientists  urge  the  adoption  of  14.5°  C.  to  15.5°  C.,  others  the 
quantity  required  to  heat  from  17°  C.  to  18°  C.,  and  many 
engineers  the  mean  value  between  0°  C.  and  100°  C.  The  logical 
way  to  settle  this  discussion  would  be  to  define  the  calorie  and  B.T.U. 
in  terms  of  the  equivalent  number  of  foot-pounds  or  other  work  units. 
This,  however,  is  not  practicable,  because  we  cannot  experimentally 
transform  mechanical  energy  into  heat  energy  with  a  greater  accuracy 
than  J  per  cent. 

12.  Relation  between  Mechanical  and  Heat  Units  and 
Electrical  and  Heat  Units.  The  units  of  quantity  of  heat 
do  not  mean  much  to  us  from  a  practical  standpoint  until 
we  have  determined  their  relation  to  the  mechanical  and 
the  electrical  units  of  energy.  There  is  no  simple  mathe- 
matical way  of  finding  the  numerical  relation.  We  have 
to  depend  upon  experimental  values. 

J.  P.  Joule,  an  English  business  man,  made  a  classical  series  of 
determinations  of  this  quantity.  The  first  of  these  was  started  about 
1841  and  the  last  in  1878.  In  Fig.  1,  page  10,  is  shown  the  essential 
details  of  his  apparatus.  The  weights  Wi}  Wz  in  falling  rotate  the 
small  drum  A  and  thereby  make  the  paddles  P  stir  the  water  in  the 
calorimeter  C.  By  withdrawing  the  pin  R  the  weights  may  be 
again  wound  up  without  moving  the  paddles.  By  repeating  this 
process  he  obtained  measurable  quantities  of  heat  energy.  This 
result  was  at  first  about  one  per  cent  lower  than  the  value  now  in 
common  use. 

Professor  H.  C.  Rowland,  of  Johns  Hopkins  University,  Baltimore, 
undertook  in  1879  to  check  Joule's  work  with  more  modern  apparatus. 
He  drove  the  paddles  by  a  steam  engine,  used  thermometers  that 
were  more  accurately  calibrated  by  comparison  with  standard  instru- 
ments, corrected  for  the  variation  of  the  heat  capacity  of  water  at 
different  temperatures,  and  in  various  other  ways  reduced  the  errors 
of  the  earlier  work. 


I.     ENERGY 


17 


Osborne  Reynolds  and  W.  H.  Moorby  in  1897  made  a  determina- 
tion, using  a  Prony  brake  with  a  water-cooled  jacket.  Their  brake  is 
shown  in  Fig.  3.  They  experienced  great  trouble  from  moisture  in 
the  insulation  material  used  to  protect  the  brake  from  loss.  They 
used  a  100  H.P.  steam  engine  to  supply  their  energy  but  while  they 
worked  with  good-sized  quantities  their  results  could  easily  have 
contained  an  error  of  \  per  cent. 

Numerous  other  methods  of  determining  the  mechanical  equiva- 
lent of  heat  by  converting  mechanical  energy  directly  to  heat  energy 
have  been  tried  with  great  care  in  the  attempt  to  establish 
experimentally  the  relation  between  the  mechanical  energy  units 


FIG.  3. — Reynolds  and  Moorby's  Prony  Brake. 

and  the  heat  energy  units.  However,  none  of  these  has  proven  so 
satisfactory  as  have  experiments  in  which  electrical  energy  is  changed 
into  heat  energy.  The  mechanical  equivalent  of  the  electrical  units 
has  been  defined  and  may  be  experimentally  applied  with  an  accuracy 
of  a  higher  order  than  is  obtainable  in  heat  experiments.  Then,  if 
the  relation  of  the  electrical  energy  units  and  the  heat  energy  units 
(i.e.  the  electrical  equivalent  of  heat)  is  obtainable  with  an  error  of 
less  than  \  per  cent,  it  gives  us  information  as  to  the  mechanical 
equivalent  of  heat. 

Professors  Hugh  L.  Callendar  and  H.  T.  Barnes,  of  McGill  Univer- 
sity, used  a  piece  of  apparatus  illustrated  in  Fig.  4,  which  gave  the 
greatest  probable  accuracy  yet  obtained.  The  apparatus  was  supplied 
with  a  continuous  stream  of  electrical  energy  which  was  delivered  in 


18 


HEAT 


the  straight  tube  A  B  to  a  platinum  wire  resistance  coil.  This  coil  is 
bathed  in  a  stream  of  liquid  (usually  water)  flowing  along  this  tube. 
As  the  liquid  enters  and  leaves  this  tube,  its  temperature  is  taken 
by  a  set  of  delicate  thermocouples,  which  are  so  connected  to  a  galva- 


M 


FIG.  4. — Electrical  Equivalent  Apparatus. 

nometer  that  the  galvanometer  deflection  is  in  proportion  to  the 
difference  in  temperature.  By  this  arrangement,  the  apparatus  may 
be  operated  under  constant  conditions  for  considerable  periods  of 
time  and  rates  of  flow  of  energy  along  the  various  possible  paths 
obtained  very  accurately. 


Wooden 


FIG.  5. — Mechanical  Equivalent  Apparatus. 

The  Searles  apparatus  shown  in  Fig.  5  is  driven  by  a  handwheel 
not  shown  in  the  cut.  The  rope  Ri,  Rz  runs  over  the  handwheel 
and  causes  the  cup  C  to  rotate.  The  meter  E  shows  the  number  of 


I.     ENERGY  19 

times  that  the  cup  C  (and  also  B,  which  moves  with  it)  is  rotated. 
Cup  A  does  not  rotate,  but  is  held  back  by  a  suitable  weight  W.  This 
weight  W  is  adjusted  until  it  is  just  enough  to  balance  the  friction 
between  cups  A  and  B.  P  is  a  thin  sheet  of  paper  introduced  be- 
tween A  and  B  to  make  the  friction  more  uniform.  To  overcome  the 
friction  between  these  two  thin  brass  cups  A  and  B,  mechanical  energy 
is  given  to  the  apparatus.  The  amount  of  energy  so  furnished  is 
obtained  as  follows:  The  work  done  against  friction  per  revolution 
equals  the  weight  in  pounds  W  times  the  circumference  of  the  pulley 
in  feet  D,  since  W  =  force  and  the  circumference  the  distance  through 
which  the  force  was  exerted,  and  f  or  ceX  distance  =  work. 

In  computing  the  work  done,  we  consider  that  D  has  moved 
relatively  to  C,  which  we  may  consider  as  remaining  in  a  fixed 
position. 

The  total  work  will  equal  the  work  per  revolution  times  the  number 
of  revolutions  or 

WX  diameter  of  DXxXrevolutions  turned  through. 

This  quantity  is  to  be  equated  to  the  heat  in  B.T.U.  's  gained  in 
the  cups.  The  heat  gained  equals  the  rise  in  temperature  of  the 
cups  and  contents,  X  the  sum  of  the  (weight  of  water  in  the  cups 
and  the  water  equivalent  of  the  cups).  (For  a  more  complete  dis- 
cussion of  the  methods  of  calorimetry  see  p.  47.) 

DATA  AND  CALCULATIONS 

Weight  of  cups  ..........................  =     .325  Ib. 

Weight  of  water  .........................  =     .0645  Ib. 

W  ..........................  ...........  =     .545    Ib. 

Diameter  of  drum  .......................  =14  ins. 

Room  temperature  ......................  =75.2°  F. 

Initial  temperature  of  water  and  cups  .....  =61.87°  F. 

Final  temperature  of  water  and  cups  .......  =88.78°  F. 

Total  revolutions  .......................  =  1020 

Rise  in  temperature  of  cups,  etc  ............  =26.91° 

Water  equivalent  of  cups  and  water  in  cups  .  =     .0970  Ib. 

Total  heat  developed  =  .0970  X26.91  ........  =  2.61  B.T.U. 


2.61  B.T.U.  =  2038  ft.-lbs. 
1  B.T.U.  =  780  ft.-lbs. 


20 


HEAT 


While  this  result  is  higher  than  the  accepted  value  for  the  mechan- 
ical equivalent  of  heat,  it  is  very  satisfactory  considering  that  there 
were  no  special  precautions  or  corrections  applied  except  to  start 

with  water  as  far  below  the 
temperature  of  the  room 
as  it  was  raised  above. 
One  per  cent  variation  is 
to  be  expected  with  this 
apparatus. 

The  resistance  coil, 
shown  in  Fig.  6,  is  used 
to  determine  the  electrical 
equivalent  of  heat.  The 
wire  is  of  a  special  alloy, 
"la  la,"  having  a  constant 
resistance  at  all  ordinary 
temperatures.  It  is  wound 
on  a  hard  rubber  frame  R. 
The  ends  are  connected  to 
the  two  posts  A,  B. 

The  coil  is  placed  in  a 
small  beaker  of  distilled 
water  and  a  known  current 
is  sent  through  it  for  a 
time  long  enough  to  raise 
the  temperature  as  far 
above  that  of  the  room 
as  the  initial  temperature 
was  below.  The  total  elec- 
trical work  done  on  the 
coil  is  written  on  one  side 
of  an  equation  and  the 
total  heat  energy  developed 
on  the  other  side.  The 
equation  is  then  simplified 
and  the  answer  appears 
in  substantially  one  of  the 
forms  shown  in  Table  II. 

Brown's  apparatus  for 
making  this  same  determination  is  shown  in  Fig.  7.  It  consists  of 
a  thirty-two  candle-power  carbon  filament  bulb  in  a  micanite 
weather-proof  socket,  into  which  is  screwed  a  short  piece  of  brass 
pipe  joined  at  the  upper  end  to  a  wooden  head.  This  head  carries  a 


FIG.  6. — Immersion  Resistance  Coil. 


I.     ENERGY 


21 


pair  of  Fahnestock  binding  posts  for  the  terminals  of  the  lamp.  All 
the  joints  about  the  lamp  socket  are  sealed  with  beeswax  to  keep 
out  moisture. 

With  the  electrical  connections  shown  in  Fig.  7,  two  sets  of  data 
are  taken,  but  only  the  set  using  the  metal  calorimeter  C  is  necessary 
for  determining  the  electrical  equivalent  of  heat.  This  calorimeter 
is  made  of  copper  and  has  a  metal  cover  as  well,  so  that  no  energy  is 
allowed  to  escape  from  the  lamp  in  the  form  of  light  or  other  radiations. 


FIG.  7. — Electrical  Equivalent  Apparatus 

DATA  AND  CALCULATIONS 

METAL  CAL. 

Weight  of  glass  in  lamp  bulb 30  gm. 

Temperature  of  room 19°  C. 

Weight  beaker,  rod  and  cover 570  gm. 

Weight  beaker,  rod,  cover,  and  water . .  2070  gm. 

Temperature  at  start 16°  C. 

Highest  temperature  of  water 23°  C. 

Time  at  start 12  hr.    2'    0" 

Time  at  finish .  .                                       .  12  hr    9'  30" 


GLASS  CAL. 

30  gm. 

21°  C. 

710  gm. 
1250  gm. 

17°  C. 

25°  C. 

llhr.  23' 30" 
11  hr.  28'    0" 


22 


HEAT 


Electric  measurements , 


VOLTS. 

AMP. 

VOLTS. 

AMP. 

105 

.99 

105 

1.00 

104 

.98 

107 

1.03 

106 

1.00 

104 

.99 

103 

.98 

105 

1.00 

107 

1.01 

105 

1.00 

105 

1.00 

104 

.98 

105 

.99 

METAL  CAL.  GLASS  CAL. 

Mean  spherical  c.p.  from  glass  calo- 
rimeter   ....  22.4 

Weight  water  and  water  equivalent ...  1525  gm.  730  gm. 

Rise  in  temperature .  . 7 . 0  C.  8 . 0°  C. 

Calories  of  heat  developed 10,670  5840 

Time  of  run  in  seconds 450  270 

Average  volts 105  105 

Average  amperes .99  1 . 00 

Total  watts  delivered  to  lamp 104  105 

Electrical  energy  used  in  watt-seconds .  46,800  28,400 
Electrical   equivalent   in    calories   per 

watt-second 236  (.206) 

or  in  watt-seconds  per  calorie 4.21  (4 . 85) 

Mechanical  equivalent  in  foot-pounds 

per  B.T.U 788  (690) 

While  this  set  of  data  and  computations  was  carried  to  three 
significant  figures,  the  third  place  represents  only  an  estimated  value, 
since  the  electrical  readings  were  accurate  to  only  one  per  cent.  No 
correction  for  radiation,  conduction,  or  convection  was  used,  but  the 
loss  was  probably  too  small  to  be  significant,  as  the  experiment  was 
started  with  the  calorimeter  at  a  temperature  as  far  below  that  of 
the  room  as  it  was  carried  above. 


GLASS  CALORIMETER 

The  second  set  of  data  gives  some  interesting  information  on  the 
amount  of  energy  that  goes  from  the  lamp  in  the  form  of  ether 
radiations.  The  value  of  the  electrical  equivalent  is  seen  to  be 
smaller  by  about  12.7  per  cent  than  the  value  obtained  in  the  previous 
set  of  data.  12.7  per  cent  of  105  watts  or  13.34  watts  therefore  were 


I.     ENERGY  23 

radiated  from  the  lamp  out  through  the  glass  calorimeter.  All  of 
these  radiations  were  not  visible  but  resulted  in  22.4  mean  spherical 
candle-power  of  visible  effect  or  light.  This  represents  a  light  flux 
of  22.4  X4x  or  282  lumens.  Then  1  watt  will  furnish  282  -r- 13.34  or 
37.6  lumens  along  with  some  other  radiations.  While  this  is  not  in 
any  accurate  sense  a  value  for  the  light  equivalent  of  1  watt  of  elec- 
trical power  it  gives  a  clue  as  to  the  rate  of  flow  of  light  energy. 

In  conclusion  it  may  be  stated  that  by  placing  a  suitable 
resistance  in  distilled  water  and  sending  current  through 
it  we  find  that  1  calorie  of  heat  energy  appears  in  the 
water  for  every  4.2  watt-seconds  of  electrical  energy  used 
up  in  the  coil.  It  has  also  been  found  that  by  stirring 
water  with  a  system  of  paddles,  1  B.T.U.  of  heat  energy 
will  be  given  to  the  water  when  780  ft.-lbs.  of  work  have 
been  done  upon  it. 

For  the  solution  of  the  succeeding  problems  it  is  well 
to  refer  to  the  appendix  for  numerical  relations  existing 
between  the  various  mechanical,  electrical  and  heat  units, 
and  much  time  may  be  saved  in  computations  if  care  is 
taken  to  select  the  most  convenient  constant.  (See  Table  II.) 

Problem  11.  A  coil  of  wire  having  a  resistance  of  20  ohms 
and  carrying  a  current  of  6  amps,  is  placed  in  a  beaker  containing 
700  gms.  of  pure  water.  Neglecting  the  heat  capacity  of  the  beaker 
how  much  rise  in  temp,  of  the  water  would  be  produced  in  49 
seconds? 

Watts  used  =  20  X  6  X  6  =      720 

Watt-seconds          =720x49    =35300 

Calories  developed  =  ~^-        =  8400 

QAf\f\ 

Rise  in  temp,  produced  in  700  gms.  =  -^-  =  12.0°  C. 

Problem  12.  A  saw  used  to  cut  marble  takes  10  H.P.  How 
much  water  must  be  supplied  per  min.  at  a  temp,  of  50°  F.  to 
keep  the  work  and  saw  at  80°  F.? 


24  HEAT 

Work  per  min.  =  10  X  33000  =  33000  f t-lbs. 

330000 
in  equivalent  heat  units  =  =     424  B.T.U. 

Each  Ib.  of  water  takes  away  30  B.T.U. 

424 
Total  water  per  min.  required  =  — —  =  14  Ibs.  2  ozs. 

Problem  13.  If  a  60-watt  lamp  is  placed  in  a  vessel  containing 
1.93  kgms.  of  water  at  20°  C.,  how  long  will  it  take  the  water 
to  come  to  the  boiling-point  if  all  the  energy  remains  in  the  water? 

Problem  14.  If  a  Prony  brake  is  found  to  be  absorbing  8 
H.P.,  and  if  cold  water  is  run  in  continuously  at  40°  F.,  and  is 
spilled  out  at  150°  F.,  how  much  water  per  minute  must  be  allowed 
to  flow  to  prevent  any  increase  in  temperature  of  the  brake? 

Problem  15.  Apparatus  is  arranged  so  that  the  energy  from 
5  kgms.  falling  through  1.860  kilometers  is  used  to  stir  93  gms. 
of  water  whose  original  temp,  was  15°  C.  What  was  the  final 
temp.? 


I.     ENERGY  25 


SUMMARY,   CHAPTER   I 

ENERGY  is  a  familiar  idea  that  is  not  readily 
defined. 

WORK  is  Quantity  of  Energy.  When  we  talk 
quantitatively  about  energy  we  use  work  units. 
The  process  of  doing  work  takes  place  when  energy 
is  transferred. 

ENERGY  Takes  Various  Forms,  such  as  the  mechan- 
ical, electrical,  light,  and  heat  forms.  These  we 
classify  into  Energy  of  Motion  and  Fixed  or  Stored 
Energy. 

HEAT  ENERGY  is  Energy  of  Motion.  The  motion 
is  molecular  and  the  total  energy  is  in  proportion  to 
the  velocity  squared  of  the  average  molecule.  The 
Total  Heat  Energy  of  a  mass  is  the  Total  Kinetic 
Energy  of  the  molecules. 

TEMPERATURE  Expresses  how  much  Hotter  or 
Colder  a  Body  is  than  some  other  Body.  Temperature 
is  relative  and  tells  which  way  we  may  expect  heat 
energy  to  be  transferred.  The  boiling-  and  freezing- 
points  of  water  are  the  ordinary  points  of  reference. 

The  RELATION  between  the  various  mechanical, 
electrical,  and  heat  energy  or  work  units  must  be 
found  experimentally. 

ONE  DEGREE  CENTIGRADE  is  -    -  of  the  differ- 

100 

ence  in  temperature  between  boiling  and  freezing  of 
water. 


26  HEAT 

ONE  DEGREE  FAHRENHEIT  is  -—•   of    this  same 

IoO 

difference.  The  ZERO  on  the  Fahrenheit  scale  is  32° 
Below  Freezing.  This  point  should  always  be  remem- 
bered in  changing  from  one  system  to  the  other. 

The  CALORIE  and  the  B.T.U.,  are  Quantity  Units 
of  heat  energy  and  consequently  are  work  units. 

A  CALORIE  is  the  Heat  Energy  Necessary  to  Raise 
1  gm.  of  Water  1°  C. 

A  B.T.U.  is  the  Heat  Energy  Necessary  to  Raise  1  Ib. 
of  Water  1°  F. 


CHAPTER  II 
ENERGY  FROM   FUELS 

13.  Fuels.  Any  substance  that  may  be  oxidized  or 
burned  and  thereby  made  to  produce  heat  energy  in  com- 
mercial quantities  is  called  a  fuel.  Practically  all  fuels  are 
made  up  of  either  pure  carbon  or  of  carbon  and  compounds 
of  carbon  formed  with  hydrogen,  nitrogen,  oxygen,  sulphur, 
etc.  Gaseous  fuels  have  no  free  carbon,  but  may  contain 
besides  carbon  compounds  uncombined  hydrogen,  nitrogen, 
oxygen,  etc.  Liquid  fuels  may  have  various  impurities  in 
mechanical  mixture  with  the  carbon  compounds.  Solid 
fuels  contain  all  of  the  above  plus  moisture,  ash,  and  a  great 
variety  of  elements  and  compounds  in  small  quantities. 
The  following  definitions  are  in  good  usage  to  classify  the 
constituents  of  coal. 

Ash.  Earthy  matter  and  other  impurities  that  remain  as  solid 
residues  after  burning  is  completed  are  classed  as  ASH.  This  subject 
has  never  been  given  the  attention  that  it  should  receive.  While  com- 
mercial coal  produces  from  4  to  25  per  cent  of  ash  in  the  case  of  the 
coals  having  the  high  per  cent  no  attempt  has  yet  been  made  to  care- 
fully study  the  chemical  changes  and  the  energy  relations  in  this  part 
of  the  fuel.  Probably  on  a  good  grade  of  coal  there  is  no  appreciable 
energy  lost  or  gained  due  to  ash.  If  the  ash  tends  to  "melt  or  fuse" 
and  form  clinker  it  is  likely  to  clog  the  grate.  Ash  always  interferes 
with  the  draft. 

Moisture.  In  a  fuel  the  uncombined  water  that  may  be  driven 
off  by  continued  heating  for  an  hour  at  a  temperature  between  105°  C. 
and  107°  C.  is  classed  as  MOISTURE.  Coal  as  mined  always  contains 
some  water.  This  may  be  increased  in  shipment  by  rain  or  by 
turning  on  a  hose.  The  water  may  also  dry  out  to  some  extent 
along  with  certain  volatile  matter.  The  heat  value  of  coal  as 
weighed  may  be  very  much  less  per  pound  than  a  dried  sample  shows 

27 


28  HEAT 

when  tested  in  a  fuel  calorimeter.  Moisture  in  coal  greatly  reduces 
its  value  as  a  fuel  because  of  the  large  quantity  of  energy  required 
to  drive  off  the  moisture.  This  energy  must  be  subtracted  from  that 
in  the  fuel  to  give  its  correct  fuel  value.  The  numerical  relations 
involved  will  appear  from  problems  to  be  solved  later.  See  Chap.  V, 
Problems  12,  13  and  18. 

Volatile  Matter.  All  of  the  constituents  of  coal  that  may  be 
driven  off  in  the  form  of  gas  before  combustion  takes  place  are 
classed  as  VOLATILE  MATTER.  From  this  quantity  it  is  usual  to  exclude 
all  water  that  may  be  dried  out  by  an  hour's  heating  at  a  temperature 
between  105°  and  107°  C.  Included,  however,  there  will  always  be 
some  carbon  dioxide,  nitrogen,  and  other  gases  which  do  not  change 
in  chemical  composition  and  consequently  do  not  generate  or  absorb 
heat.  The  sample  is  slowly  brought  to  red  heat  in  a  closed  crucible. 
If  no  oxygen  is  allowed  to  reach  the  sample  no  burning  will  take  place. 

Fixed  Carbon.  All  the  combustible  mass  remaining  after  the 
volatile  matter  is  driven  off  is  called  FIXED  CARBON.  This  is  usually 
obtained  by  subtracting  the  ash  from  the  total  residue  after  the  volatile 
matter  is  driven  off. 

An  Ultimate  Chemical  Analysis,  if  at  all  complete,  should  show 
the  percentage  of  carbon,  hydrogen,  nitrogen,  oxygen,  sulphur,  and 
ash.  Frequently  the  percentages  of  phosphorus,  iron,  pyrites,  etc.,  are 
required  before  the  suitability  of  a  given  fuel  for  a  given  purpose  can 
be  determined. 

A  Complete  Chemical  Analysis  should  give  the  compounds  and 
elements  in  the  per  cent  in  which  they  exist  in  the  sample  as  received. 

A  Proximate  Analysis  should  show  the  moisture,  fixed  carbon, 
volatile  matter,  ash,  and  sulphur. 

Classification  of  Solid  Fuels  into  various  grades  and  sizes  of  anthra- 
cite, bituminous  coal,  lignite,  and  peat  is  on  a  commercial  rather  than 
a  scientific  basis,  and  the  reader's  general  experience  will  contribute  an 
adequate  understanding  of  the  distinction  between  the  various  kinds. 

Coke  is  the  residue  obtained  by  driving  off  the  volatile  matter 
from  coal  (usually  some  form  of  bituminous). 

Charcoal  is  the  residue  obtained  by  driving  off  the  volatile  matter 
from  wood.  Both  coke  and  charcoal  contain  all  the  ash,  therefore, 
all  the  solid  impurities  of  the  original  fuel. 

Liquid  Fuels.  The  various  hydrocarbon  compounds  that  go  to  make 
up  mineral  oil  are  the  liquid  fuels  most  commonly  used.  Much  oil  in  the 
crude  state  and  a  constantly  increasing  amount  of  alcohols  are  used. 

Since  liquid  fuels  have  to  be  vaporized  before  they  are  burned, 
they  are  really  used  as  gaseous  fuels,  but  are  more  conveniently  handled 
as  liquids. 


II.     ENERGY  FROM  FUELS  29 

Gaseous  Fuels.  In  some  localities  natural  gas  is  available  but, 
in  general,  gas  is  made  from  coal  or  liquid  fuels.  A  proximate  chemical 
analysis  of  the  type  usual  for  coals  and  other  solid  fuels  is  valuable, 
but  it  does  not  indicate  definitely  the  fuel  value  of  a  liquid  or  a  gas. 
If  the  complete  chemical  analysis  gives  the  per  cent  of  the  various 
compounds  and  elements  in  the  fuel,  a  very  accurate  estimate  of  the 
fuel  value  can  then  be  made.  For  illustration  a  purified  producer 
gas  would  contain,  nitrogen  (N),  oxygen  (O2),  hydrogen  (H2),  carbon 
monoxide  (CO),  carbon  dioxide  (CO2),  and  methane  (CH4).  So-called 
"coal  gas"  will  have  in  addition  to  the  above:  Ethylene  (C2H4), 
illuminants,  and  occasionally  water,  hydrogen  sulphide  (H2S),  benzine 
(C6H8),  etc.  From  an  analysis  giving  the  per  cents  of  each,  the  fuel  value 
may  be  computed  by  referring  to  Table  III,  for  the  fuel  value  of  each 
of  the  constituent  compounds  and  multiplying  by  the  proper  per  cent. 

Powdered  Fuels.  Fuels  are  frequently  pulverized  and  blown  with 
an  air  blast  into  furnaces  used  for  metallurgical  purposes.  By  this 
plan  coals  that  clinker  badly  on  a  grate  and  that  are  low  in  heat  value 
can  be  profitably  burned.  Coals  high  in  volatile  matter  give  especially 
good  results  when  pulverized. 

14.  Air  in  Chemical  Reactions.  In  the  every-day  use 
of  fuels  we  support  their  combustion  by  supplying  oxygen 
(O)  from  the  air.  Besides  oxygen  air  contains  nitrogen 
(N),  which  is  an  inactive  gas  and  does  not  change  its  state 
or  in  any  way  enter  into  the  chemical  reactions.  This 
nitrogen  serves  no  useful  purpose,  but  dilutes  the  oxygen 
and  is  extra  matter  that  has  to  be  moved  and  heated  without 
any  useful  result.  (See  Chapter  III,  Section  25  and 
Problems  34  and  35.) 

Air  is  about  I  oxygen  and  f  nitrogen,  but  it  also  contains 
a  variable  amount  of  moisture,  carbon  dioxide  (CC>2)  and 
in  small  quantities  hydrogen  (H),  helium  (He),  argon  (A), 
etc.  In  ordinary  computations  of  the  amount  of  air  required 
to  burn  a  given  amount  of  fuel,  the  composition  of  dry  air 
may  be  taken  as  20.7  per  cent  O,  and  79.3  per  cent  N  by 
volume,  or  23  per  cent  O  and  77  per  cent  N  by  weight. 

As  soon  as  CO2  is  formed,  it  is  also  considered  as  an  inert 
gas  like  N,  and  no  energy  can  be  obtained  from  it. 

Carbon  monoxide  is  a  poisonous  gas.  When  heated 
to  above  600°  F.  in  the  presence  of  oxygen  it  burns  to  CO2- 


30  HEAT 

Below  this  temperature  it  acts  as  an  inert  gas  like  CC>2 
andN. 

The  minimum  proportion  in  which  elements  combine 
is  given  in  tables  of  "  Atomic  Weights." 

The  common  elements  found  in  fuels  with  their  atomic 
weights  are: 

Hydrogen  (H) 1.008 

Oxygen  (0) 16.00 

Carbon  (C) 12.00 

Sulphur  (S) 32.06 

Phosphorus  (P) 31 .00 

Hydrogen  burns  with  oxygen  to  water  (H20),  2.016 
gms.  of  H  unite  with  16  grams  of  O  and  18.016  gms. 
of  H2O  result. 

12  gms.  of  C  unite  with  16  gms.  of  0  to  produce  28  gms. 
of  CO;  12  gms.  of  C  unite  with  32  gms.  of  O  to  produce 
44  gms.  of  C02.  When  burning  a  fuel  with  a  hot  fire  and 
with  a  plentiful  supply  of  oxygen  no  CO  is  formed,  but  only 
C02.  If  there  is  a  scant  supply  of  oxygen,  conditions  are 
more  favorable  for  the  formation  of  CO. 

15.  Energy  Involved  in  All  Chemical  Reactions.  Table 
III  in  the  back  of  the  book  gives  the  energy  developed  by 
oxidization  of  carbon  and  some  of  its  compounds  that  are 
commonly  found  in  fuels. 

It  is  a  veiy  important  fact  that,  associated  with  the  for- 
mation of  not  only  products  of  burning,  such  as  carbon 
dioxide,  carbon  monoxide,  water,  etc.,  but  also  with  the 
formation  of  every  other  chemical  compound,  there  is  also 
a  giving  or  taking  of  energy.  This  fact  may  be  stated  even 
more  generally  by  saying  that  with  every  chemical  change 
there  is  a  giving  or  taking  of  energy. 

A  compound  which  absorbs  heat  energy  during  formation  is  said 
to  be  "endothermic."  A  compound  which  gives  up  heat  energy 
during  formation  is  called  "exothermic."  This  text  deals  mainly  with 


II.      ENERGY  FROM  FUELS  31 

the  heat  energy  transformed,  but  there  may  be  electrical  energy  trans- 
formed as  well. 

From  the  above  statement  it  follows  that  the  amount 
of  energy  which  a  compound  will  give  up  when  oxidized  or 
burned  depends  somewhat  upon  how  much  was  taken  on 
or  given  off  when  the  compound  was  formed. 

For  example,  acetylene  has  the  chemical  formula  C2H2 
and  benzine  CeHe.  Now  one  would  expect  equal  weights 
of  these  two  compounds  to  develop  equal  quantities  of  heat 
energy,  but  1  Ib.  of  acetylene  gives  as  much  energy  as  1.18 
Ibs.  of  benzine.  For  exact  values  see  Table  IV. 

16.  Heat  Energy  of  Fuels.  All  our  most  accurate 
knowledge  of  the  energy  changes  that  go  with  chemical 
changes  are  derived  from  experiments.  The  methods  of 
determining  the  energy  liberated  from  fuels  are  discussed 
in  Chapter  VII,  together  with  the  descriptions  of  the  various 
calorimeters,  etc.,  used. 

The  heat  energy  relations  associated  with  the  oxidation 
of  chemical  elements  and  the  more  common  organic  com- 
pounds have  been  carefully  determined,  and  a  few  of  these 
are  to  be  found  in  Table  IV.  These  determinations  enable 
us  to  compute  the  fuel  value  of  liquids  and  gases  when  we 
have  a  complete  chemical  analysis  and,  from  an  approximate 
analysis  giving  the  per  cent  of  elements,  we  can  make  a 
rough  estimate  of  the  energy  available  in  coals.  These 
computations  are  very  important  in  flue  gas  tests,  gas 
generator  tests,  furnace  tests,  etc. 

The  following  formulae  give  a  close  approximation  of 
the  energy  available  in  coals  and  are  based  on  ultimate 
analysis,  including  moisture. 

Calories  per  gm.  =8080(C-  0.120XO) 

+34460(H- 0.063  XO)+2250S, 

B.T.U.  per  lb.  =  14540(C-0.120XO) 

+62030(H-0.063XO)+4050S. 


HEAT 

The  last  factor,  is  frequently  neglected,  as  the  greater 
part  of  sulphur  remains  in  the  ash  when  combustion  takes 
place  on  a  grate. 

The  following  problems  will  illustrate  the  use  of  these 
formulae  and  the  tables. 

Problem  1.  How  many  B.T.U.  should  sample  No.  1  in 
Table  IV  develop? 

Substituting  in  our  formula  we  have: 

B.T.U.  =[14540(70.73  -  0.120  X  8.67)  +62030(4.87 -0.063  X  8.67) 

+  4050X  .94] -r- 100 

=  [14540(69.69)  +  62030  X  4.31  +40]  -=- 10 ) 
=  12840. 

Problem  2.  Compute  the  calories  per  gram  developed  from 
sample  No.  2  in  Table  IV. 

Cal.  =  [8080(68.69 -0.120  X  11. 49) +34460(4.84- 0.063  X  11.49) 

+  2250X  1.01] -T- 100 

=  [8080(67.31)  +34460(4.12)  +  23]  -MOO 
=  5439+1420+23 

=  6882 

Problem  3.  From  Gas  Analysis  No.  1,  Table  V,  compute  the 
B.TJtF.  per  cubic  foot  of  this  sample  of  producer  gas: 

B.T.U.  =  338(CO)  +  348(H)  +  1052(CH4) 

=  338X  .112+348X  .06+  1052X  .089 
=  37.8+20.9+93.6 
=  152.3  per  cu.  ft. 

Problem  4.  Suppose  the  coal  in  Problem  1  is  burned  in  a 
furnace  under  a  boiler  and  the  fire-box  ashes  analyzed  with  the 
following  result:  Carbon  18.8  per  cent,  ash  81.2  per  cent.  Find 
the  energy  lost  in  the  ashes  per  pound  of  coal  used. 

The  pounds  of  coal  per  pound  of  fire-box  ashes  will  be  obtained 
by  dividing  the  per  cent  of  true  ash  in  the  ash  from  the  fire-box 
by  the  per  cent  of  ash  in  the  coal,  or  81.2  -=-13.41  =  6.06  Ibs. 

Carbon  wasted  per  pound  of  coal  =  18.8%  -=-  6.06  =  3.10%, 

Energy  wasted  per  pound  of  coal  =  14540  X  .031  =  453  B.T.U. 

Problem  5.  9.17  Ibs.  of  air  were  used  to  burn  each  pound  of 
coal  in  Problem  1,  and  if  the  following  analysis  by  weight  of  the 


II.     ENERGY  FROM  FUELS  33 

flue  gases  resulted,  find  the  heat  lost  up  the  stack  in  the  com- 
bustible gases: 

CO  =  1.0% 
C02=22.1 
CH4=     .2 
H20=  4.4 
0=  2.4 
N=69.9 
100.0  % 

In  10  Ibs.  of  gaseous  products  of  combustion  for  1  Ib.  of  coal, 
we  have, 

10  Ibs.  CO  X    4393  =439.3  B.T.U.  lost  in  C02, 
.02  Ib.  CH4  X  23560  =471.2  B.T.U.  lost  in  CH4 
Total,  910.5  B.T.U.  lost  up  stack. 

Problem  6.  Find  the  heat  value  of  the  coal  in  Table  IV, 
Sample  3,  in  B.T.U.  per  pound. 

Problem  7.  In  Problem  6  substitute  in  the  formula  for  the 
calories  per  gram  and  give  the  relation  that  exists  between  the 
calories  and  B.T.U. 

Problem  8.  From  the  gas  analysis  of  Sample  No.  2,  Table  V, 
find  the  calories  per  liter  developed  upon  oxidation. 

Problem  9.  From  the  analysis  of  No.  3  in  Table  V,  find  the 
B.T.U.  per  cubic  foot  developed  during  burning. 

Problem  10.  If  a  coke  shows  2.78  per  cent  water,  .74  per  cent 
volatile  matter,  83.35  per  cent  fixed  carbon,  2.49  per  cent  sulphur, 
and  13.13  per  cent  ash,  how  many  B.T.U.  per  pound  will  it 
develop? 

17.  Explosives.  An  explosion  consists  of  one  or  more 
sudden  changes  in  pressure.  An  explosive  is  that  which 
produces  the  explosion.  High  pressures  which  characterize 
most  explosions  are  usually  due  to  a  very  rapid  burning  of  a 
fuel  in  a  confined  space.  The  essential  conditions  for 
such  an  explosion  are:  First,  an  intimate  proximity  of  the 
necessary  quantities  of  oxygen  and  combustible;  second, 
the  formation  of  gaseous  products  of  combustion,  and 
third,  the  transformation  of  chemical  energy  into  heat 
energy  in  large  enough  quantities  to  heat  the  gaseous 
products  of  combustion  to  a  high  temperature. 


34  HEAT 

Cotton  we  do  not  think  highly  of  as  a  fuel.  Under  normal  con- 
ditions it  burns  slowly  with  a  great  quantity  of  smoke.  However, 
if  cotton  is  soaked  with  liquid  air,  or  better,  liquid  oxygen,  and  ignited, 
it  may  burn  as  quickly  as  gunpowder  and  with  as  little  smoke.  Thus 
an  explosion  is  largely  a  question  of  having  an  intimate  mixture  of 
oxygen  and  combustible. 

A  common  type  of  combustible  entering  into  explosions 
is  the  gas  given  off  from  solid  or  liquid  fuels  and  the  pure 
gaseous  fuels,  like  water  gas,  natural  gas,  producer  gas,  etc. 
None  of  these  will  explode  until  mixed  with  oxygen.  People 
who  like  to  do  spectacular  things  frequently  throw  lighted 
matches  into  liquid  fuels.  This  produces  no  disastrous 
results  if  there  is  no  explosive  mixture  of  gases  above  the 
liquid.  The  pure  fuel  will  extinguish  the  match,  because 
the  match  itself  must  have  oxygen  to  burn.  In  most  cases: 

An  explosive  is  an  intimate  mixture  of  oxygen  and  a  fuel. 

The  explosion  engines  of  to-day  all  use  a  mixture  of  air  and  a  gas 
made  from  some  fuel.  The  successful  running  of  the  engine  demands 
that  at  the  time  that  the  explosion  is  started  the  gaseous  fuel  be 
thoroughly  mixed  with  air  in  a  suitable  proportion.  A  detailed  dis- 
cussion of  how  this  is  arranged  belongs  properly  in  the  chapter  on 
gas  engines  and  will  be  further  discussed  there. 

The  effect  of  the  explosions  may  be  greatly  reduced  by  mixing 
with  the  explosives  an  inert  gas  like  nitrogen,  carbon  dioxide,  or  steam. 
Thus  in  the  gas  engines  it  is  necessary  to  sweep  out  of  the  cylinder 
all  products  of  previous  explosions,  else  they  will  dilute  the  incoming 
charge  and  also  tend  to  cushion  the  explosion. 

The  explosion  is  more  effective  when  the  explosive  is  heated  to  a  high 
temperature  before  explosion  takes  place.  There  are  two  reasons  for 
this:  First,  because  the  total  amount  of  heat  energy  after  the  explo- 
sion is  greater,  and,  second,  because  the  time  necessary  for  the  chemical 
reaction  to  be  completed  and  for  the  energy  to  be  transformed  is 
shortened  by  increasing  the  temperature.  The  violence  of  an  explosion 
is  both  a  matter  of  the  amount  of  heat  energy  released  and  the  time 
required  to  completely  transform  this  from  fixed  chemical  energy  to 
heat  energy. 

Explosives  for  use  in  firearms,  mines,  quarry  work,  etc.,  are  divided 
into  two  classes: 

Explosive  mixtures, 
Explosive  compounds. 


II.     ENERGY  FROM  FUELS  35 

Explosive  mixtures  like  gunpowder  have  separate  compounds, 
one  of  which  contains  oxygen  mixed  physically.  In  gunpowder  we 
may  have  70  or  80  per  cent  of  charcoal  mixed  with  some  sulphur  and 
10  or  12  per  cent  of  potassium  nitrate.  The  nitrate  contains  oxygen 
which  when  the  mixture  is  heated  is  given  off  to  combine  with  the 
charcoal  and  form  CO2,  K2CO3,  CO,  N,  and  various  other  compounds 
are  also  formed. 

In  the  explosive  compounds,  such  as  nitroglycerine  and  nitro- 
cellulose, all  the  necessary  material  for  burning  is  within  each  mole- 
cule. Nitroglycerine  has  the  chemical  formula,  C3H5(NO3)3,  and  two 
molecules  of  it  break  up  in  accordance  with  the  equation, 

2C3H5(NO3)3  =  6CO2  +  5H2O  +  3N2  +  O. 

In  this  case  fifteen  gaseous  molecules  result  from  two  liquid  mole- 
cules, and  since  they  are  at  first  formed  in  the  space  occupied  by  the 
two  liquid  molecules,  they  are  under  great  pressure.  This  pressure 
is  increased  by  the  large  amount  of  heat  energy  transformed  during 
the  chemical  reaction. 

The  effectiveness  of  these  compounds,  however,  lies  chiefly  in  the 
fact  that,  since  the  rearrangement  is  largely  between  atoms  inside 
one  molecule,  the  process  is  completed  in  an  extremely  short  space  of 
time.  The  disruptive  effect  increases  greatly  with  a  decrease  of 
time.  This  fact  leads  to  a  classification  of  explosive  compounds  as 
high  explosives  and  fulminates  in  contrast  to  the  slow-burning  gun- 
powders and  other  physical  mixtures. 

18.  Exceptional  Fuels.  Various  metals  such  as  magnesium,  iron, 
zinc,  etc.,  can  be  burned.  This  property,  in  the  case  of  mag- 
nesium, is  much  taken  advantage  of  to  make  Flashlights,  which  are 
mild  explosives,  giving  a  light  strong  in  the  ultraviolet  rays.  No 
more  spectacular  application  of  knowledge  of  chemical  and  energy 
relations  has  been  made  than  the  application  of  Thermite  to  emer- 
gency repair  and  difficult  welding.  Thermite  is  both  the  fuel  and 
the  solder.  Oxides  of  iron,  magnesium,  chromium,  and  other  metals, 
and  aluminium  powder  are  mixed  and  placed  in  contact  with  the 
parts  to  be  welded.  When  ignition  takes  place  the  aluminium  takes 
the  oxygen  away  from  the  other  metals  with  evolution  of  great  heat. 
This  heat  melts  the  iron  or  steel  surfaces  against  which  it  rests  and 
the  metals  in  the  thermite  join  the  iron  of  the  broken  piece.  The 
aluminium  oxide  tends  to  float  to  the  surface  and  leave  a  solid  metal 
joint.  In  this  compound  we  have  an  explosive  mixture  which  produces 
mainly  a  solid  product  of  combustion  and  consequently  there  is  not 
such  a  pronounced  tendency  toward  expansion.  The  amount  of  heat 


«3b  HEAT 

given  off  for  any  given  percentage  of  aluminium  powder  and  oxides 
may  be  computed  from  Table  III. 

19.  Purchasing  Coal.  In  purchasing  coal  it  is  clear  that, 
other  things  being  equal,  what  we  want  to  get  is  the  maximum 
amount  of  energy  for  the  money  expended.  However, 
there  are  always  other  considerations  besides  the  energy 
contained.  Some  coals  tend  to  form  clinker  and  cause 
trouble  and  extra  labor  in  firing.  If  the  coal  contains  con- 
siderable quantities  of  sulphur  it  may  form  corrosive  com- 
pounds. Soft  coal  burns  more  freely  than  hard  coal  and  there 
is  frequently  a  great  deal  of  choice  between  varieties  when 
boilers  are  to  be  forced,  because  of  firing  qualities.  In  any 
particular  furnace  some  types  of  coal  will  be  found  to  work 
.better  than  others,  and  so  the  choice  is  sometimes  limited 
to  a  great  extent  by  the  conditions  imposed. 

Any  fuel  may  be  burned  successfully  in  a  properly 
designed  furnace  if  the  following  conditions  are  fully 
met: 

1.  Fuel  must  be  supplied  uniformly  over  the  grate  sur- 
face and  as  nearly  continuously  as  possible. 

2.  An  air  supply  must  be  provided  somewhat  in  excess 
of  the  amount  theoretically  required.     This  should  not  all 
be  forced  through  the  fuel  bed  in  the  case  of  fuels  giving  off 
large  quantities  of  volatile  matter. 

3.  A  temperature  above  the  fuel  bed  sufficiently  high  to 
ignite  the  gases  driven  off  from  fuel  is  required. 

4.  Before  these  gases  reach  any  cooling  surface  such  as 
the  shell  or  tubes  of  a  boiler  they  must  be  mixed  with 
air  and  complete  combustion  must  take  place. 

In  anthracite  coal  usually  90  per  cent  of  the  combustible 
constituents  is  fixed  carbon.  It  follows  that  the  fuel  value 
is  mainly  affected  by  the  percentage  of  moisture  and  ash. 
As  anthracite  coal  furnished  for  household  purposes  fre- 
quently contains  as  high  as  25  per  cent  ash  and  10  per  cent 
moisture  when  delivered,  it  is  readily  seen  that  the  purchasers 


II.     ENERGY  FROM  FUELS  37 

may  effect  considerable  savings  by  giving  these  matters 
attention. 

20.  Heat  Engine.    A  heat  engine  is  any  machine  which 
transforms  heat  energy  into  mechanical  energy.     In  common 
use  we  have  but  two  varieties,  the  steam  engine  and  the 
explosion  engine,  although  the  hot-air  engine   is  sometimes 
used.* 

The  steam  engine  draws  into  its  cylinder  under  pressure 
a  hot  gas  which  has  a  quantity  of  heat  energy  in  it  due 
to  its  temperature  and  its  pressure.  From  this  charge  of 
hot  gas  the  steam  engine  takes  and  transforms  a  small  part 
of  the  energy  into  the  mechanical  form. 

The  explosion  engine  draws  into  its  cylinder  a  charge  of 
cold  combustible  gas  and  air  which  is  burned  in  the  cylinder, 
forming  very  hot  gases  as  products  of  the  burning.  The 
chemical  energy  of  the  gaseous  fuel  is  converted  in  the  cylin- 
der to  heat  energy  and  from  this  supply  of  heat  energy 
work  is  done  by  the  engine.  The  theory  is  essentially  the 
same  for  all  explosion  engines  whether  they  burn  alcohol, 
gasolene,  kerosene,  crude  oil,  natural  gas,  coal  gas,  or 
producer  gas.  Practically  there  is  great  difference  in  the 
design  and  construction  of  these  engines  using  the  various 
fuels,  due  to  the  peculiarities  of  each  fuel. 

21.  Power  Plant.     Any  combination  of  apparatus  that 
transforms  energy  from  a  fixed  or  stored  form  or  from  an 
unavailable  kinetic  form  into  available  energy  of  motion  is  a 
power  plant. 

For  example,  a  steam  power  plant  transforms  the 
energy  of  some  fuel  into  mechanical  energy  by  first  giving 
the  energy  to  water,  which  in  gaseous  form  conveys  the 
energy  to  an  engine.  The  engine  completes  the  trans- 
formation. 

An  hydro-electric  power  plant  transforms  the  potential 
and  kinetic  energy  of  water  into  mechanical  energy  and  the 

*  The  "naphtha  launch"  really  has  a  variety  of  steam  engine. 


38  HEAT 

dynamos  transform  the  mechanical  energy  into  electrical 
energy. 

Output 

22.  Efficiency  =  —      — .     This  is  the  familiar  brief  form 
Input 

of  the  definition  of  efficiency.  The  following  is  a  more 
complete  statement: 

The  efficiency  of  a  system  or  machine  is  the  simultaneous 
ratio  between  the  energy  taken  in  and  that  given  out.  Input  and 
output  may  be  expressed  either  in  work  units  (determined 
for  a  fixed  time)  or  in  power  units.  Preferably  the  same 
unit  should  be  used  in  numerator  and  denominator  when 
the  efficiency  should  be  stated  in  per  cent.  While  this 
is  the  clearest  and  most  logical  way  of  expressing  the  result, 
commercially  efficiency  is  frequently  expressed  by  using  a 
mixture  of  units.  Thus  the  efficiency  of  a  power  plant  is  often 
given  in  pounds  of  coal  per  horse-power  hour  of  output. 

One  pound  of  a  given  coal  represents  nearly  as  definite 
a  quantity  of  energy  as  one  horse-power  hour.  If  the  B.T.U. 
per  pound  of  coal  is  known,  the  result  obtained  in  horse-power 
hours  per  pound  of  coal  can  easily  be  computed  to  a  per  cent 
basis.  This  is  done  in  Problem  1  below.  In  a  similar 
way  boiler  efficiency  is  commonly  expressed  in  pounds  of 
water  evaporated  from  and  at  212°  F.  per  pound  of  coal 
burned.  This  again  can  be  reduced  to  a  per  cent  basis 
when  the  energy  in  the  coal  is  known.  See  Chapter  VI  for 
a  discussion  of  problems  of  this  character. 

In  technical  literature  there  is  only  one  common  instance 
of  the  use  of  efficiency  in  any  sense  other  than  that  given 
above.  In  the  field  of  illumination,  "  efficiency  "  of  electric 
lamps  is  stated  as  watts  (a  power  unit)  per  candle  power 
(a  unit  of  intensity  or  intrinsic  brilliancy  of  a  light  source). 
This  gives  a  high  value  for  a  poor  lamp  and  a  low  value  for 
a  good  lamp,  reversing  the  ordinary  usage  of  the  word. 

Problem  11.  A  producer  gas  power  plant  burns  1.21  Ibs.  of  coal 
testing  13,200  B.T.U.  per  pound  for  each  horse-power  hour 
delivered  by  the  engine.  Find  the  efficiency  of  the  plant  in  per  cent. 


II.     ENERGY  FROM  FUELS  39 

Reducing  both  to  foot-pounds  of  work  we  have 

Output      =  1  H.P.  hour  =  33000  X  60 
Input        =1.21X13200X778 

33000  X  60 
1.21X13200X778 

Problem  12.  A  steam  power  plant  has  an  efficiency  of  8.2  per 
cent  and  delivers  each  24  hours  12,400  H.P.  hours  of  work.  Find 
the  amount  of  coal,  analyzing  13,800  B.T.U.  that  will  be  used 
per  day. 

Energy  given  out  per  day  equals 

12400  X  33000  X  60  ft.-lbs. , 

If  x  =  the  pounds  of  coal  per  day  the  energy  used  per  day  will  be 
13800  X  778  X  z  ft.-lbs., 

12400  X  33000  X  60 
Efficiency  •     138Q()  x  77g  x  ^    =.082, 

12400  X  33000  X  60     0_nr 
*  =  13800  X  778  XW  =279°°  ^  °f  C0al  per  ^ 

Problem  13.  A  steam  electric  power  plant  transforms  1  k.w.  hour 
of  energy  from  1.12  Ibs.  of  coal  containing  14,300  B.T.U.  per  Ib. 
Find  the  efficiency  in  per  cent. 

Problem  14.  How  many  horse-power  hours  should  an  explosion 
engine  having  an  efficiency  of  22  per  cent  develop  per  gallon  of 
gasoline? 

Problem  15.  How  many  hours  will  a  60  H.P.  gasoline  engine 
of  22  per  cent  efficiency  run  on  10  gals,  of  gasoline? 

Problem  15A.  How  much  ethyl  alcohol  per  horse-power  hour 
is  required  in  an  engine  of  20  per  cent  efficiency? 


40  HEAT 


REVIEW   PROBLEMS,    CHAPTER   II 

16.  How  many  B.T.U's.  are  required  to  raise  the  temperature 
of  195  Ibs.  of  water  from  32°  F.  to  212°  F.? 

17.  How  many  foot-pounds  of  energy  would  it  take  to  do  the 
work  in  above  problem? 

18.  How  many  calories  would  it  take  to  raise  1800  grams  of 
water  from  0°  C.  to  82°  C.? 

19.  A  certain  heat  engine  has  an  efficiency  of  11  per  cent.     In 
burning  5  Ibs.  of  coal,  how  much  work  can  it  do?     (1  Ib.  of  coal 
gives  out  14,000  B.T.U's.) 

20.  If  engine  in  Problem  19  burns  the  5  Ibs.  of  coal  in  1  hour 
what  horse-power  is  developed? 

21.  A  locomotive  while  burning  120  Ibs.  of  coal  is  able  to  draw  a 
400-ton  train  2  miles  up  a  grade  of  20  ft.  to  the  mile.     Assuming 
friction  as  10  Ibs.  to  the  ton,  what  is  the  efficiency  of  the  locomo- 
tive? 

22.  If   it  takes  10  minutes  to  go   the   2  miles    in  the  above 
example,  what  must  the  horse-power  of  locomotive  be? 

23.  The  flow  of  water  from  tailrace  of  a  mill  is  1000  cu.ft.  per 
minute.     If  the  head  of  water  is  12  ft.,  what  horse-power  will  a 
water-wheel  have  which  utilizes  6  per  cent  of  the  energy  supplied 
by  the  water? 

24.  How  many  pounds  of  coal  would  a  heat  engine  require  per 
hour  to  generate  the  above  horse-power,  assuming  an  efficiency  of 
20  per  cent? 

25.  An  incandescent  lamp  uses  50  watts  of  electricity,  88  per 
cent  of  which  is  given  off  in  heat.     How  many  calories  of  heat 
are  thus  given  off  in  one  hour? 

26.  An  engine  is  able  to  do  70  million  foot-pounds  of  work  by 
burning  112  Ibs.  of  coal.     How  many  pounds  of  coal  does  it  con- 
sume per  horse-power  hour? 

27.  What  is  the  efficiency  of  the  engine  in  Problem  11? 

28.  How  many  foot-pounds  of  work  in  1  Ib.  of  coal  containing 
12,000  B.T.U.? 

29.  How  many  horse-power  hours  of  work  are    in    1    ton   of 
coal  containing  12,500  B.T.U.  per  pound? 

30.  How  many  kilowatt  hours  in  1  ton  of  coal  containing 
13,200  B.T.U.  per  pound? 


II.     ENERGY  FROM  FUELS  41 

31.  How  many  pounds  of  water  must  be  held  at  a  height  of 
100  ft.  to  store  an  amount  of  energy  equal  to  that  contained  in 
1  Ib.  of  coal  yielding  13,800  B.T.U.? 

32.  If  it  takes  approximately  400  B.T.U.  per  hour  to  keep  up 
the  natural  processes  in  our  body  and  if  as  a  power  plant  we  have 
an  efficiency  of  25  per  cent,  how  many  B.T.U's.  per  day  must  be 
taken  into  our  body  to  keep  the  plant   itself  running? 

33.  A  man  does  work  at  the  rate  of  .24  H.P.  for  5  hours  a  day 
and  500  B.T.U.  per  hour  are  required  to  keep  up   his    natural 
processes.     If  he  neither  gains  nor  loses  weight,  and  his  efficiency 
as  a  power  plant  is  20  per  cent,  how  many  B.T.U.'s  must  he  take  in? 

Assume  the  .24  H.P.  to  be  used  outside  the  body.  ' 

34.  A  power  plant  has  12  per  cent  efficiency  and  when  run  at 
its  maximum  capacity  delivers  1800  kw.     Find  its  coal  consump- 
tion per  day. 

35.  A  steam  plant  uses  1.5  Ibs.  of  coal  per  horse-power  hour. 
Find  the  theoretical  plant  efficiency  if  each  pound  of  coal  contains 
13,600  B.T.U. 

36.  A  power  plant  has  a  coal  consumption  when  run  at  full 
capacity  of  25  tons  per  day.     If  its  efficiency  is  10  per  cent,  how 
many  horse-power  does  it  develop? 

37.  Assuming  an  efficiency  of  5  per  cent,  how  far  up  a  grade  of 
24  ft.  to  the  mile  will  300  Ibs.  of  coal  take  a  train  weighing  400  tons? 
Friction  =  10  Ibs.  per  ton. 

38.  If  distance  in  Problem  22  is  covered  in  one-half  hour,  what 
average  horse-power  is  developed  by  the  engine? 

39.  How  many  pounds  of  coal  does  the  engine  in  Problem  22 
burn  per  horse-power  hour? 

40.  How  far  will  a  pound  of  coal  containing  13,200  B.T.U. 
propel  a  train  and  locomotive  weighing  400  tons  against  a  rolling 
friction  of  8  Ibs.  per  ton,  if  all  the  heat  energy  is  used  to  do  work? 

41.  If  the  average  plant  efficiency  of  an  Edison  electric  illumi- 
nating company  is  12  per  cent,  and  if  they  pay  $3  per  long  ton 
for  a  coal  which  contains  12,400  B.T.U.  per  pound,  what  does  it 
cost  the  company  for  fuel  per  kilowatt  hour  "generated"? 

42.  If  mechanical  energy  is  being  transformed  into  heat  energy 
at  the  rate  of  12  H.P.,  how  many  B.T.U.  per  hour  will  result? 

43.  24  H.P.  equals  how  many  calories  per  minute? 

44.  10  kw.  equals  how  many  calories  per  second? 

45.  Various   experimenters   have   determined   the   amount   of 
energy  received  by  the  earth  from  the  sun,  and  it  is  fairly  well 
established  that  outside  the  earth's  atmosphere  between  3  calories 
and  3.5  calories  are  received  per  minute  per  square  centimeter 


42  HEAT 

of  surface  normal  to  the  sun's  rays.  If  2.5  calories  per  minute 
per  square  centimeter  reach  the  earth,  how  many  B.T.U.  per 
square  foot  per  mimute  does  this  represent? 

46.  If  11  B.T.U.  per  square  foot  per  minute  are  received,  how 
many   square   feet   of  area  would  apparatus  receiving  10  H.P. 
require? 

47.  Apparatus  exposing  1000  sq.ft.  of  surface  receives  on  the 
average  during  a  ten-hour  day,  5  B.T.U.  per  square  foot  per 
minute.     If  the  apparatus  transforms  the  energy  received  into 
mechanical  energy  with  an  efficiency  of  2  per  cent,  what  average 
horse-power  is  developed  during  the  10  hours? 

48.  If  a  city  lot  20x100  ft.  receives  energy  at  the  average 
rate  of  4  B.T.U.  per  square  foot  per  minute  for  10  hours  per  day 
and  25  days  per  month,  how  many  tons  of  coal  per  month,  each 
pound  containing  12,000  B.T.U.,  would  supply  an  equal  amount 
of  energy? 

49.  If  the  apparatus  in  the  previous  problem  were  used  to 
transform  the  energy  into  mechanical  energy  and  operated  with 
an  efficiency  of  4  per  cent,  how  many  horse-power  would  be  de- 
veloped? 

50.  Consider  the  total  area  of  the  earth  receiving  energy  to 
equal   (5280)  2X  (4000)  2X  3.14  sq.ft.,   and  the  population  of  the 
earth  to  equal  10,000,000,000.     How_many  horse-power  per  human 
being  are  received  if  3.5  calories  per  minute  per  square  centimeter 
be  taken  as  the  rate? 


II.     ENERGY  FROM  FUELS  43 

SUMMARY,   CHAPTER   II 

FUELS  are  substances  which  burn  and  give  off 
stored  or  fixed  energy  in  the  form  of  heat  energy. 

A  PROXIMATE  ANALYSIS  shows  the  per  cent  of 
moisture,  fixed  carbon,  volatile  matter,  ash,  and 
sulphur  in  a  fuel. 

AN  ULTIMATE  ANALYSIS  shows  the  percentage 
of  each  of  the  elements  in  a  fuel. 

FUELS  require  oxygen  from  the  air  to  burn  and 
the  products  contain  amounts  by  weight  of  their 
elementary  (atomic)  constituents  in  proportion  to 
atomic  weights  of  the  elements  combined. 

EVERY  CHEMICAL  REACTION  that  takes  place  is 
accompanied  by  a  taking  of  energy  in  the  heat  form 
(and  sometimes  in  the  electrical  form  as  well). 

PURCHASING  COAL  is  a  matter  of  buying  an 
amount  of  fixed  energy  in  the  chemical  form  and  not 
a  weight  or  mass  of  material.  Care  must  be  used 
to  see  that  the  coal  is  adapted  to  the  furnace  in  which  it 
is  to  be  burned. 

A  HEAT  ENGINE  transforms  heat  energy  into  mechan- 
ical energy. 

A  POWER  PLANT  transforms  the  fixed  or  stored 
energy  of  fuel  or  the  mechanical  energy  of  the  wind, 
tide,  or  river,  or  the  heat  energy  o/  the  sun  into  avail- 
able mechanical  energy  of  motion  or  electrical  energy. 

OUTPUT 
EFFICIENCY  =  INPUT  -    The  output  and  the  input 

are  always  taken  at  the  same  time;  hence  time  is  not 
a  factor  in  defining  efficiency.  A  machine  or  a  plant 
efficiency  is  a  ratio  between  the  work  given  out  and  the 
work  taken  in. 


CHAPTER  III 
SPECIFIC   HEAT  AND   CALORIMETRY 

23.  Specific  Heat.  One  B.T.U.,  if  applied  to  a  pound 
of  lead  at  room  temperature  will  cause  a  rise  in  temperature 
of  about  33°  F.;  if  applied  to  a  pound  of  aluminum,  4.7°  F.; 
if  applied  to  a  pound  of  water,  1°  F.;  and  if  applied  to  a 
pound  of  ice,  originally  at  0°  F.,  one  B.T.U.  will  warm  the 
ice  to  approximately  2°  F.  It  appears,  then,  that  equal 
quantities  of  heat  energy  added  to  a  unit  mass  of  various 
substances  do  not  produce  an  equal  rise  in  temperature. 
The  heat  energy  seems  to  fill  up  some  substances  faster 
than  others,  and  so  we  think  of  each  element  and  compound 
as  having  its  own  distinct  "  heat  capacity." 

It  is  customary  to  take  the  heat  capacity  of  water  as 
the  standard,  and  compare  other  substances  with  it.  The 
heat  capacity  or  specific  heat  of  a  substance  is  the  ratio 
between  the  amount  of  heat  energy  required  to  raise  the 
temperature  of  a  mass  of  the  substance  one  degree  and  the 
amount  of  heat  energy  necessary  to  raise  an  equal  mass  of 
water  one  degree. 

Using  English  units  and  for  convenience  taking  1  Ib. 
of  a  substance: 

B.T.U.  of  heat  energy  to  raise  1  Ib.  of  substance  1°  F. 
B.T.U.  of  heat  energy  to  raise  1  Ib.  of  water  1°  F. 

But  the  heat  energy  to  raise  1  Ib.  of  water  1°  F.  =  l  B.T.U. 
Therefore,  numerically,  Sp.H.  =  B.T.U.  of  heat  energy  to 
raise  1  Ib.  of  the  substance  1°  F. 

44 


Sp.H. 


III.     SPECIFIC  HEAT  AND  CALORIMETRY         45 

Similarly,  using  metric  units: 

Calories  of  heat  energy  to  raise  1  gm.  of  substance  1°C. 


Calories  of  heat  energy  to  raise  1  gm.  of  water  1°  C. 


But  the  heat  energy  to  raise  1  gm.  of  water  1°  C.  =  l  calorie. 

Therefore,  numerically,   Sp.H.  =  calories    to  raise  1  gm.  of 

substance  1°  C. 

Accordingly,  the  following  is  true  numerically: 
Specific  heat  =  hesit  energy  to  raise  unit  weight  1°. 

Problem  1.  A  cast-iron  bearing  weighs  20  kgms.  How 
many  calories  will  heat  it  from  12°  C.  to  200°  C.?  How  many 
watt  hours?  (Assume  no  energy  lost.) 

Specific  heat  of  the  iron  =  .12; 

Calories  per  degree.  .  .  .  =  20000  X.  12  =2400 

Calories  for  188°  ......  =2400  X  188  =450000  calories 

Watt  seconds  .........  =450000  X4.2 

450000  X4.2      _on 
=  53Q' 


Problem  2.  How  many  heat  units  are  required  to  raise  the 
temperature  of  300  Ibs.  of  lead  from  32°  F.  to  56°  F.? 

Specific  heat  of  lead  =  .031. 

It  requires  .031  B.T.U.  to  raise  1  Ib.  1°. 

Therefore  it  requires  300  X.031  =9.3  B.T.U.  to  raise  300  Ibs.  1°. 

It  requires  9.3  X  (56  -32)  =9.3x24=223  B.T.U.  to  raise  300 
Ibs.  24°  or  from  32°  F.  to  56°  F. 

Problem  3.  How  many  foot-pounds  of  work  would  be  necessary 
to  produce  the  temperature  change  on  the  300  Ibs.  of  lead  in 
Problem  2? 

1  B.T.U.  =  778  ft.-lbs., 

223  B.T.U.  =223  X778  =  173,000  ft.-lbs. 

Problem  4.  How  many  calories  to  raise  4  Ibs.  of  aluminium 
from  0°  C.  to  328°  F.?  (Specific  heat  of  aluminium  =  .212.) 

Problem  5.  How  many  B.T.U.  are  required  to  raise  the  tem- 
perature of  one  ton  of  water  from  40°  F.  to  water  at  382°  F.? 

Problem  6.  How  many  foot-pounds  of  mechanical  energy 
would  it  take  to  do  the  work  in  the  above  problem?- 


46 


HEAT 


Problem  7.  How  many  calories  will  raise  20  Ibs.  of  air  from 
10°  C.  to  25°  C.  under  standard  conditions  of  pressure? 

Problem  8.  How  many  B.T.U.  are  required  to  heat  12  Ibs.  of 
air  from  60°  F.  to  the  temperature  of  a  furnace  fuel  bed  known 
to  be  at  2300°  F.?  Assume  the  specific  heat  of  air  to  average 
.240  for  this  range  of  temperature. 

Problem  9.  How  much 
energy  would  be  required 
to  heat  1  Ib.  of  coal  from 
60°  F.  to  2300°  F.,  if  the 
specific  heat  of  the  coal 
over  this  range  equals  .22? 
Problem  10.  A  cast- 
iron  fly-wheel  is  fitted  with 
a  Prony  brake  equipped 
with  cast-iron  shoes.  If 
wheel  and  shoes  weigh 
100  Ibs.  and  8.3  H.P.  is 
being  absorbed,  how  much 
rise  in  temperature  in  5 
minutes  if  no  heat  were 
lost? 

Problem  11.  How 
many  B.T.U.  per  hour 
will  it  be  necessary  to  ex- 
tract from  the  air  to  cool 
an  auditorium  132  X  70 
X  28,  when  the  average 
temperature  of  the  air 
drawn  out  is  85°  F.  and 
the  air  returned  43°  F.?  Assume  the  air  to  have  an  average 
density  of  .0685  Ib.  per  cubic  foot  and  the  entire  volume  of  air 
displaced  once  per  hour. 

Problem  12.  How  many  people,  each  giving  off  400  B.T.U. 
per  hour,  must  sit  in  this  auditorium  if  the  temperature  -does  not 
change? 

Specific  Heat  is  Not  a  Constant.  The  specific  heat 
of  any  element  or  substance  is  not  a  constant,  but 
changes  when  the  temperature  rises,  and  when  a  change 
of  state,  crystalline  structure  or  density  takes  place.  An 
examination  of  the  table  of  specific  heats  in  the  back  of. 


1.0175 
1.0150 
1.0125 
1.0100 
1.0075 
1.0050 
1.0025 
1.000 
.9975 

Kelation  between  the 
Specific  Heat 
and 
Temperature 
of  Water 

I 

\ 

/ 

\ 

/ 

/ 

\ 

\ 

•/_ 

/ 

20°      0°        20°       40°        60°       80°      HX 

FIG.  8. 

III.     SPECIFIC  HEAT  AND  CALORIMETRY          47 

the  book  will  illustrate  these  points.  Notice  particularly 
carbon  and  water.  Fig.  8  shows  the  variation  in  the  specific 
heat  of  water  between  the  freezing-  and  boiling-points. 

Specific  heat  is  a  ratio  whose  value  is  independent  of  the  size  of 
the  unit  of  mass  and  the  units  of  temperature  and  quantity  used, 
because  each  unit  appears  as  a  factor  an  equal  number  of  times  in  both 
numerator  and  denominator  and  consequently  cancels  out. 

For  a  discussion  of  the  specific  heat  of  gases  see  Chapter  VIII. 

24.  Calorimetry.  A  CALORIMETER  is  any  piece  of  appara- 
tus used  to  measure  quantity  of  heat  energy.  This  name 
is  applied  to  a  great  variety  of  apparatus  so  that  the  only 
thing  it  designates  is  the  use  to  which  the  article  is  put. 
Calorimeters  are  usually  very  simple  copper  vessels  which 
may  be  protected  from  drafts,  radiation,  etc.,  by  an  outer 
vessel  or  jacket.  Fuel  calorimeters  are  frequently  elaborate 
platinum-lined  steel  bombs.  Steam  calorimeters  are  some- 
times little  more  than  a  steam  pipe,  with  pressure  gauge, 
valve  and  exhaust  chamber  containing  a  thermometer. 

Calorimetry  in  a  simple  form  is  illustrated  by  the 
METHOD  OF  MIXTURES.  The  method  gets  its  name  from 
the  fact  that  two  substances  like"  lead  shot  and  water  or 
iron  and  water  are  mixed  together.  These  substances  (or 
two  quantities  of  the  same  substance)  are  at  different  but 
known  temperatures  before  mixing.  They  are  allowed  to 
come  to  the  same  temperature  after  mixing  and  this  tem- 
perature is  determined. 

The  assumption  is  made  that  no  heat  is  lost  to  outside 
bodies,  and  an  equation  is  based  upon  this  assumption. 
This  equation  may  be  written  in  either  of  two  ways: 

1.  Heat  gained   BY   THE   COLD  BODIES  =  heat    lost   BY 
HOT  BODIES. 

2.  Total  heat  IN  ALL  BODIES  before  MIXING  =  total  heat 

IN  ALL  BODIES  after  MIXING. 

Total  heat  above  32°  F.  of  any  body  =  (its  temperature 
Fahrenheit  —  32°)  XweightXits  specific  heat. 


48  HEAT 

The  first  equation  is  the  simplest  to  write  except  when 
steam  is  involved.  Since  some  students  in  the  class  may 
already  be  in  the  habit  of  using  this  equation,  it  is  preferable 
that  all  should  use  it  in  problems  not  involving  steam. 

In  practice,  the  engineer  most  frequently  employs  the  second  style 
of  equation  in  steam  problems,  because  it  is  much  more  convenient. 
It  is  therefore  suggested  that  the  student  habitually  use  this  second 
type  of  equation  for  steam  boiler  and  engine  problems. 

Engineers  usually  write  this  equation,  using  the  total  heat  above 
32°  F.  (or  0°  C.),  and  this  practice  should  also  be  followed  by  the 
student. 

When  this  suggestion  is  carried  out  consistently,  the  student  finds 
that  in  some  problems  he  has  to  express  heat  in  a  body  colder  than 
the  freezing  temperature  as  a  minus  quantity.  While  there  is  no 
such  thing  as  a  minus  quantity  of  heat,  the  expression  has  meaning 
when  used  to  indicate  the  condition  of  a  body  having  less  energy  in  it 
than  the  body  has  at  the  standard  temperature,  32°  F. 

25.  Water  Equivalent.  The  calorimeter  itself  always 
contains  a  certain  amount  of  energy  which  may  be  expressed 
by  its  weight  X  specific  heat  X  temperature,  if  its  specific 
heat  is  known.  The  capacity  of  a  calorimeter  to  absorb 
heat  is  therefore  expressed  by  its  weight  times  its  specific 
heat.  This  product  is  known  as  the  water  equivalent  of  the 
calorimeter.  Most  calorimeters  are  made  of  sheet  copper, 
nickel  plated,  and  they,  usually  have  a  specific  heat  approx- 
imately equal  to  .10.  It  is  the  common  practice  in  ordinary 
laboratory  work  to  take  the  water  equivalent  =  .10X  weight. 
No  significant  error  results  in  any  laboratory  experiment 
when  this  practice  is  followed.  Weigh  the  thermometer 
with  the  calorimeter  and  treat  it  as  a  part  of  the  calorimeter. 

If,  however,  extreme  accuracy  is  desired,  or  the  calorim- 
eter is  constructed  of  a  variety  of  materials  of  unknown 
specific  heat,  the  water  equivalent  may  be  found  as  in  the 
determination  that  follows; 


III.     SPECIFIC  HEAT  AND  CALOBIMETRY          49 

DATA 

A  calorimeter  weighs 108.2  grams. 

Cold  water  is  put  in  it  when 

Calorimeter  and  cold  water  weighs 242 .'6  grams. 

Some  hot  water  is  prepared  in  a  vessel  directly  above 
the  calorimeter  and  kept  at  a  temperature  of 
100°  C. 
Just  before  adding  hot  water  observation  is  taken 

and: 

Temperature  of  calorimeter  and  contents  before  =   10.2°  C. 
Hot  water  is  at  once  added  and  after  rapidly  stirring, 

observations  were  made  as  follows : 

Temperature  of  calorimeter  and  contents  after..  .  =  31.6°  C. 
Weight  of  calorimeter  and  contents  after  mixture  =288.1  grams. 

COMPUTATIONS 

Let  the  water  equivalent  of  the  calorimeter  =x. 
The  total  heat  in  calorimeter  and  cold  water  was 

(x+ 134.4)  X  10.2  calories. 
The  total  heat  in  the  hot  water  added  was 
45.5  X  100  calories. 

The  total  heat  in  the  calorimeter  and  co/itents  after  mixing  the 
hot  and  cold  water  must  have  been 

(a; +  179.9)  X  31.6°  calories. 
Writing  the  total  heat  equation,  we  have 

(z  + 134.4)+  10.2  +  45.5  X  100  =  (a; +  179.9)  X  31.6. 

Solving: 

10.2x  +  1371  +  4550  =  31. Ox  +  5685; 

21.4&=236, 

x  =  10.98  grams  water  equivalent. 
Just  as  in  the  above  experiment,  the  water  equivalent  is 


50  HEAT 


always  added  to  the  weight  of  the   water  in  the  calorimeter 
when  water  is  used. 

26.  Precautions  in  Calorimetry.  Not  only  in  calo- 
rimetry by  the  method  of  mixtures,  but  in  all  calorimetry, 
variations  in  the  numerical  results  may  be  due  to  causes 
falling  under  three  classes: 

(a)  True  errors  resulting  from  careless  work  by  the  experi- 
menters. 

(b)  Errors  due  to  weakness  in  the  method  of  experimen- 
tation. 

(c)  Variation  in  the  quantities  to  be  measured  due  to 
factors  not  under  the  control  or  under  the  observation  of 
the  experimenter. 

ERRORS  OF  CLASS  (a)  must  be  reduced  by  the  exercise 
of  great  care  and  attention  to  details.  Each  temperature 
reading  and  each  weighing  should  be  carefully  inspected  until 
the  experimenter  is  sure  that  all  differences  in  weight  and  all 
differences  of  temperature  are  known  to  the  desired  number 
of  significant  figures. 

Among  the  errors  of  this  class  that  the  student  should 
especially  guard  against  and  keep  constantly  in  mind  are 
the  following: 

1.  Inaccurate  reading  of  thermometers.     The  eye  must 
be  on  a  level  with  the  top  of  the  mercury  column  in  the  stem 
when  readings  are  taken.     The  thermometer  may  be  given 
a  slight  mechanical  vibration  to  counteract  the  tendency 
for  mercury  to  stick  and  go  up  or  down  by  jumps. 

2.  Too  great  haste  in  taking  temperatures.     If  temper- 
atures are  read  too  quickly,  the  thermometer  does  not  have 
time  to  reach  the  temperature  of  its  surroundings. 

3.  Taking  the  temperature  of  a  part  of  a  liquid  or  body. 
In  case  of  a  liquid  this  should  be  guarded  against  by  thor- 
oughly stirring  immediately  before  reading  the  temperature. 

4.  Adding  heat  to  the  calorimeter  or  other  apparatus 
by  holding  it  in  the  hand,  over  a  radiator,  near  a  lamp,  or 


III.      SPECIFIC  HEAT  AND  CALORIMETRY          51 

other  body  considerably  warmer  than  the  body  itself.  It 
is  equally  important  not  to  take  away  heat  by  placing  the 
calorimeter  on  the  table  or  iron  base  of  ring  stands,  etc.  Wooden 
stands  are  provided  upon  which  the  calorimeter  may  be 
supported  with  very  little  metal  surface  in  contact  with 
the  wood.  If  these  with  the  calorimeter  are  placed  inside 
an  insulated  chamber  to  cut  off  air  drafts,  the  calorimeter 
will  be  well  enough  protected  for  ordinary  purposes. 

5.  Loss  of  heat  in  transferring  heated  bodies  to  the 
calorimeter.     This  operation  must  be  planned  and  practiced 
until  it  can  be  done  quickly,  neatly,  and  especially  without 
the  spilling  of  a  drop  of  liquid. 

6.  Gain  or  loss  of  heat  by  transferring  thermometers 
and  stirring  rods  back  and  forth  between  apparatus  at 
different  temperatures.     Thermometers  enough  should  be 
used  to  enable  the  experimenter  to  keep  one  constantly  in 
the   calorimeter.     The   student   may   illustrate   the   result 
of  carelessness  in  this  matter  by  reading  the  room  tem- 
perature with  a  wet  thermometer  and  then  with  a  dry  ther- 
mometer. 

ERRORS  OF  CLASS  (b)  may  be  avoided  in  part  by  the 
exercise  of  care  and  foresight.  Under  this  head  fall: 

1.  Correction  for  "  water  equivalent,"  which  has  already 
been  discussed. 

2.  Corrections  for  inaccurate  thermometers:    For  prac- 
tical work,  each  thermometer  should  be  standardized  and 
occasionally  checked  against  a  reliable  standard  or  by  rede- 
termining   its  fixed  points.     (See  Experiments  H  1-1   and 
H  1-3  and  text  on  Thermometers.) 

In  experiments  where  differences  in  temperature  only 
are  required  rather  than  exact  temperatures,  good  results 
may  follow  from  using  an  inaccurate  thermometer  provided 
it  is  evenly  divided,  of  uniform  bore,  and  the  differences  of 
temperature  not  great.  In  that  case  it  will  act  like  a  dif- 
ferential thermometer.  If  two  or  more  thermometers  are 
used  in  the  same  experiment  their  scales  should  be  compared, 


52  HEAT 

and  if  any  differences  appear  the  readings  should  be  recorded 
as  observed.  Later  they  should  be  corrected  to  values  equal- 
ing those  temperatures  which  would  have  been  read  if  the 
most  accurate  thermometer  had  been  used  for  all  the  readings. 

3.  Corrections  for  radiation.  The  calorimeter  and  con- 
tents may  gain  from  surrounding  bodies  or  may  lose 
to  these  bodies  heat  due  to  radiation.  (See  Chap.  VII.) 
This  error  may  be  largely  eliminated  by  having  the  calorim- 
eter and  its  contents  as  far  below  the.  room  temperature 
during  half  the  time  the  experiment  is  being  conducted  as 
it  goes  above  the  room  temperature  during  the  remainder 
of  the  time.  To  render  this  possible,  it  is  usual  to  make 
a  preliminary  test  to  get  in  mind  all  the  necessary 
details.  If  the  rate  of  change  of  temperature  is  fairly 
constant  during  the  experiment,  the  loss  in  one  half  the  time 
will  equal  the  gain  in  the  other  half  and  no  significant  error 
will  result.  This  means  of  correction  should  always  be  taken 
unless  conditions  forbid  it. 

Whenever  the  method  given  above  is  not  convenient,  a 
radiation  curve  should  be  plotted  and  corrections  made 
from  it.  When  this  is  carefully  done,  the  error  due  to 
radiation  will  usually  be  corrected  with  great  accuracy. 

The  following  experiment  will  illustrate  this: 

DETERMINATION  OF  THE  SPECIFIC  HEAT  OF  ALUMINIUM 

The  laboratory  directions  for  Experiment  32-1  were  followed 
in  every  particular.  After  the  aluminium  was  heated  in  a  steam- 
jacketed  chamber,  readings  of  the  thermometer  were  taken  every 
half  minute  for  five  minutes  and  a  curve  plotted,  as  shown  in  the 
figure,  from  which  to  correct  for  radiation. 

The  following  is  an  extract  from  the  laboratory  direction  sheet 
for  Experiment  H  2-1 : 

DETERMINATION  OF  THE  SPECIFIC  HEAT  OF  A  SOLID 

The  method  here  given  is  known  as  the  "Method  of  Mixtures." 
The  solid  at  some  convenient  temperature  is  placed  in  a  known 
quantity  of  water  at  a  different  temperature,  and  the  two  allowed 
to  come  to  a  common  temperature. 


III.     SPECIFIC  HEAT  AND  CALORIMETRY         53 

Data  to  be  taken  include:  (a)  Mass  of  solid;  (6)  mass  of 
water;  (c)  temperature  of  solid  before  it  is  placed  in  water;  (d) 
temperature  of  water;  (e)  temperature  of  mixture.  Correction 
must  be  made  for  any  heat  absorbed  or  given  out  by  the  calorimeter, 
which  undergoes  the  same  temperature  changes  as  the  water,  and 
some  means  must  be  employed  to  correct  for  gain  or  loss  of  heat 
through  radiation. 

Weigh  the  solid,  then  suspend  it  in  the  vessel  to  be  heated. 

In  the  meantime,  put  into  a  calorimeter  enough  water  *  cooled 
to  3°  or  4°  below  the  temperature  of  the  room,  to  cover  the  solid. 

Stir  the  water  in  the  calorimeter  thoroughly  and  take  the 
temperature.  Determine  also  the  temperature  of  the  solid  in  the 
heater.  Quickly  transfer  the  solid  to  the  calorimeter.  Stir  the 
water  until  the  temperature  ceases  to  rise,  and  record  the  highest 
temperature. 

From  your  data  compute  the  specific  heat  of  the  solid,  making 
proper  corrections  for  the  water  equivalent  of  the  calorimeter  and 
for  any  errors  of  thermometers  used.  Make  three  determinations, 
taking  the  average.  Write  complete  "heat  equations"  for  each 
computation. 

DATA 

Metal  used,  Aluminium.  Weight,  184  fl^s. 

Thermometer:    In  calorimeter — Special  20-35°. 

In  hot  water— 60  Y. 
Calorimeter  No.    Weight  108.2.    Water  equivalent  11.0  gms. 

Weight  of  calorimeter  and  cold  water,  304.6.  Weight  of  cold 
water,  196.4.  Temperature  of  hot  metal,  99.6°  C. 

*  The  exact  amount  of  water  to  be  used  and  its  temperature  will 
depend  upon  the  kind  and  weight  of  solid  used.  The  conditions 
should  be  such  that  the  temperature  of  the  water  in  the  calorimeter 
after  adding  the  solid  shall  be  as  much  above  the  room  temperature 
as  it  was  below  it  before  adding  the  solid.  Further  correction  for 
radiation  will  then  be  unnecessary.  A  preliminary  test  or  two  should 
be  made  to  determine  the  amount  of  cold  water,  and  the  temperature 
which  will  best  give  these  conditions. 


54 


HEAT 


Time. 

0 

i 

1 

li 

2 

2* 


Temp,  of 
Cold  Water. 

20.24 
24.68 
29.12 
32.85 
32.91 
32.86 


Time. 

3 

3i 

4 


Temp,  of 
Cold  Water. 

32.73 
32.56 
32.39 
32.13 
31.98 


Cooling  Curve 
for  Exp.  32-1 


The  solid  line  in  Fig.  9  represents  the  actual  readings. 

Curve  CD  is  a  short 

/  radiation    curve    for  the 

calorimeter  and  is  pro- 
jected upward  to  BE  in 
the  direction  that  the 
curve  would  probably 
have  taken  if  at  zero  time 
the  calorimeter  had  been 
at  a  somewhat  higher 
temperature  than  the 
maximum  reached  during 
the  experiment.  AMB  is 
the  curve  that  might  have 
resulted  if  the  transfer  of 

22  \J 1 1 1 1 1 1       energy  had  gone  on  at  a 

uniform  rate  until  com- 
plete and  the  temperature 
of  the  water  had  been 
instantly  indicated  on  the 
thermometer.  B,  the  inter- 
section with  the  radiation 
curve,  and  AM  extended,  would  then  have  been  the  first  point  on 
the  radiation  curve. 

The  slope  of  the  curve  BD  at  B  gives  the  velocity  of  cooling 
(due  to  radiation,  etc.)  at  B.  The  mean  velocity  of  cooling  (due 
to  radiation,  etc.,  and  tending  to  reduce  the  rise  in  temperature), 
between  A  and  B  is  only  half  of  this.  However,  we  assume  that 
the  amount  of  the  losses  due  to  radiation,  etc.,  is  in  proportion 
to  the  difference  in  temperature  between  the  vessel  and  its  sur- 
roundings. (See  Chap.  IX.)  On  this  assumption,  the  correction 
for  radiation,  etc.,  might  be  taken  as  half  the  rate  at  B  X  the 
time  to  arrive  at  B  counted  from  the  beginning  of  the  experi- 
ment. Mathematically,  this  is  exactly  equal  to  the  rate  at  B 
X  half  the  time.  If,  then,  we  project  DCB  backward  to  the 


234 
Time  in  Minutes 

FIG.  9. 


III.      SPECIFIC  HEAT  AND  CALORIMETRY          55 

point  E,  which  has  an  abscissa  half  as  large  as  B,  we  have  the 
equivalent  of  this  mathematical  process.  The  point  E  will 
represent  the  temperature  that  would  have  been  reached  and 
maintained  indefinitely  if  there  had  been  no  lost  energy  due  to 
radiation,  convection,  conduction,  etc. 

The  actual  ordinate  of  E  obtained  by  carrying  this  out 
graphical!}7  to  a  large  scale  is  33.70°  C.  From  this  value  and 
the  data  given  above  we  can  write  our  heat  equation: 

Let  X  =  specific  heat  of  aluminium. 

Heat  gained  =heat  lost. 

(196.4+  11)(33.70-  20.24)  =  184(99.6  -  33.7)X, 
207.4  X  13.46  =  184  X  65.9Z, 


The  corresponding  total  heat  equation  would  be 

(196.4+  11)20.24+  99.6  X  184  X  X 

=  (196.4+  11)33.70+  33.70  X  184  X  X. 

4.  Evaporation  of  water.  This  loss  will  be  better  under- 
stood after  a  study  of  latent  heat.  It  is  not  significant  if 
the  temperature  of  the  water  used  is  below  40°  C.,  if  the 
calorimeter  is  covered,  and  if  the  time  of  the  experiment  is 
short.  If  other  liquids  than  water  are  used,  they  should 
also  be  kept  well  below  their  boiling-point  if  errors  due  to 
evaporation  are  to  be  avoided.  The  "  radiation  curve  " 
corrects  for  this  loss  also. 

It  appears  from  the  foregoing  discussion  of  errors  of 
class  (b)  that  foresight  and  care  must  be  exercised  to  insure 
accurate  results  in  heat  experiments.  This  is  also  true  of 
errors  of  class  (c). 

(c)  DEVIATIONS  :  Variations  in  the  quantities  to  be  meas- 
ured due  to  the  fluctuations  in  the  properties  of  the  sub- 
stances studied  should  be  anticipated  and  detected  if  possible. 
Thus  fuel  calorimetry  is  resorted  to  in  order  to  detect  the 
variations  in  energy  per  pound  of  coal  or  other  fuel.  Devia- 


56  HEAT 

tions  in  specific  heat  of  substances  result  when  the  temper- 
ature is  changed,  when  the  structure  or  state  is  changed,  and 
when  even  small  per  cents  of  impurities  are  introduced.  As 
an  illustration  of  such  deviations  look  up  carbon,  water, 
mercury,  etc.,  in  the  specific  heat  tables. 

27.  Other  Methods.  Numberless  other  so-called 
"  methods  "  are  used.  They  all  differ  as  to  the  details  of 
construction  of  the  calorimeters  and  the  particular  ways 
that  are  devised  to  reduce  the  deviations  and  errors  dis- 
cussed in  the  previous  section.  The  student  will  find  that 
if  he  examines  the  manipulation  of  any  particular  calorim- 
eter and  the  computation  of  the  results  with  the  points 
already  discussed  in  mind,  no  special  difficulty  will  be  found. 

Special  calorimeters  and  their  use  are  described  in  the 
chapter  on  instruments. 

Problem  12.  Suppose  we  mix  in  a  tank  40  Ibs.  of  water  at 
120°  F.,  and  60  Ibs.  of  water  at  35°  F.,  what  will  be  the  resulting 
temperature? 

Let  x  =the  final  temperature. 

Heat  gained   by  60  Ibs.  =heat  lost  by  40  Ibs. 

60(s  -35)  =  40(120  -  .r), 
.60* -2100  =4800-40o;, 
lOOx  =  6900 
z=69°. 

The  corresponding  "total  heat"  solution  is 

Each  pound  at  120°  F.  contains  88  B.T.U.,  total  heat  above 

32°  F.,  so  40  Ibs.  contains  40  X  88  =3420  B.T.U.     Similarly, 

at  35°  F.  each  pound  contains  only  3  B.T.U.  and  60  Ibs. 

3X60  =  180  B.T.U. 
Total  B.T.U.  above  32°  F.  in  mixture  is  therefore  3420+180 

=  3600  B.T.U. 

Total  weight  of  mixture  =  100  Ibs. 
Temperature   above   32°   F.   of  mixture  =3600  -=-100  =36°   F. 

Therefore  the  final  temperature  of  mixture  =36°  F.  +  32°  F. 

=  68°. 


III.     SPECIFIC  HEAT  AND  CALORIMETRY         57 

Problem  13.  It  is  desired  to  find  the  temperature  of  a  furnace. 
A  piece  of  fire-clay  (sp.  heat  .22)  weighing  4  Ibs.  is  placed  in  a 
furnace  until  it  comes  up  to  the  temperature  of  the  furnace.  It  is 
then  dropped  into  a  pail  containing  20  Ibs.  of  water  at  40°  F. 
The  water  then  rises  to  120°  F.  What  is  the  temperature  of  the 
furnace? 

Let  *=the  furnace  temperature. 

Heat  gained  =heat  lost, 
20  X  (120  -40)  =  .22X4(«-120), 
.88* -105.6  =20X80, 
.88*=  1706, 
t  =  1938. 

The  corresponding  total  heat  solution  is: 
Before  mixture: 

Total  heat  in  water  above  32°  =20  X  8  =  160  B.T.U. 
Total  heat  in  clay    above  32°  =4  X  .22  x(t  -32)  B.T.U. 
Alter  mixture: 

Total  heat  in  water  above  32°  =20  X  88  =  1760  B.T.U. 
Total  heat  in  clay  above  32°    =4  X  .22  X  88  =77. 
Since  the  quantity  of  heat  energy  has  not  changed 

160  +4  X.  22  x(t  -32)  =1760+77, 

.88(*-32)=1677, 

.88* -28  =  1677, 

.88*  =  1705, 

*  =  1938. 

Problem  14.  If  5  Ibs.  of  water  at  200*  F.  are  mixed  with  12  Ibs. 
at  50°  F.,  what  is  the  resulting  temperature? 

Problem  15.  A  copper  calorimeter  weighs  120  gms.  In  it  are 
placed  400  gms.  of  water  at  12°  C.  Into  this  was  dropped  800  gms . 
of  pure  nickel  at  100  C°.  Find  resulting  temperature. 

Problem  16.  A  copper  calorimeter  weighs  .88  Ib.  In  it  is  placed 
5.81  Ibs.  of  water.  A  piece  of  aluminium  at  100°  C.  weighing 
7.41  Ibs.  was  dropped  into  the  water,  which  was  at  10.2°  C.,  and 
the  temperature  of  the  mixture  was  29.4°  C.  Find  the  specific  heat 
of  aluminium? 


58  HEAT 

Problem  17.  9.07  gms.  of  benzine  are  burned  in  a  fuel  calo- 
rimeter containing  18.20  Ibs.  of  water  and  having  a  water  equiva- 
lent of  .80  Ib.  The  initial  temperature  of  the  water  was  71.27°  F., 
and  the  final  temperature  was  91.82°  F.  Find  the  B.T.U.  per 
pound  of  this  sample. 

Problem  18.  A  1-gm.  sample  of  coal  is  burned  in  a  fuel  calo- 
rimeter having  a  water  equivalent  of  .56  Ib.,  and  containing  2.48  Ibs. 
of  water.  The  original  temperature  was  67.89°  F.,  and  the  final 
temperature  was  81.24°  F.  Find  B.T.U.  per  pound. 

Problem  19.  A  1-gm.  sample  of  coal  is  burned  in  a  fuel  calo- 
rimeter which  was  made  of  820  gms.  of  copper  and  4230  gms. 
of  steel.  It  contained  4820  gms.  of  water  at  21.87°  C.  before  the 
fuel  was  burned  and  the  temperature  increased  to  23.41°  C.  Find 
calories  per  gram  of  coal. 

Problem  20.  1.22  cu.ft.  of  gas  (measured  under  standard  con- 
ditions) was  burned  in  a  fuel  calorimeter  containing  8.12  Ibs.  of 
water  and  having  a  water  equivalent  of  .58  Ib.  The  products  of 
combustion  and  radiation  carried -away  4.2  B.T.U.  The  tem- 
perature before  the  run  was  62.1°  F.,  and  after  the  run  was  91.8°  F. 
Find  B.T.U.  per  cubic  foot. 


III.     SPECIFIC  HEAT  AND  CALORIMETRY         59 


REVIEW   PROBLEMS,   CHAPTER   III 

21.  Show  that  the  specific  heat  is  the  same  whatever  the  system 
of  weights  and  whatever  the  temperature  scale  used. 

22.  An  iron  ball  weighing  6  Ibs.  is  heated  in  boiling  water  at 
212°  F.,  and  then  dropped  into  4  Ibs.  of  water  at  35°.    Tem- 
perature rises  to  60°  F.    What  is  specific  heat  of  the  iron? 

23.  10  Ibs.  of  water  at  180°  F.  are  poured  into  a  copper  beaker 
weighing  2  Ibs.  and  containing  8  Ibs.  of  water  at  50°  F.    What  is 
resulting  temperature?     (Sp.  heat  copper  =  .095.) 

24.  An  aluminium  block  weighing  150  gms.  at  a  temperature  of 
100°  C.  is  dropped  into  a  copper  beaker  weighing  200  gms.,  and 
containing  400  gms.  of  water  at  10°  C.     Resulting  temperature 
is  16.4°  C.     What  is  specific  heat  of  aluminium? 

25.  Two  pounds  of  aluminium  at  50°  F.,  4  Ibs.  of  copper  at 
100°  F.,  and  10  Ibs.  of  cast  iron  at  200°  F.,  are  all  simultaneously 
plunged  into  3  cu.ft.  of  water  at  40°  F.    What  is  the  final  tem- 
perature of  the  mixture? 

26.  One  gram  of  coal  was  tested  in  a  Thomson  calorimeter 
whose  total  water  equivalent  was  2120  gms.    The  initial  and  final 
temperatures   of  the   apparatus  were  54.00°  F.,  and  60.85°  F. 
What  was  the  calorific  value  of  the  coal? 

27.  A  boiler  containing  5  tons  of  water  at  a  temperature  of 
200°  F.  is  supplied  with  water  at  60°  F.  from  a  feed-pump  deliver- 
ing 20  gals,  per  minute.     If  the  pump  be  kept  running  for  ten 
minutes,  what  will  be  the  resulting  temperature  of  the  boiler? 

28.  A  number  of  brass  condenser  tubes  weighing  540  Ibs.  were 
at  a  temperature  of  58°  F.  before  the  condenser  was  at  work; 
afterward,  when  in  use,  the  mean  temperature  was  110°  F.    How 
many  B.T.U.  did  they  take  up? 

29.  What  weight  of  water  is  the  metal  in  the  above  problem 
equivalent  to  with  respect  to  its  capacity  for  heat? 

30.  A  cast-iron  plate  weighing  120  Ibs.  is  immersed  in  240  Ibs. 
of  water.     If  the  temperature  of  the  plate  is  150°  F.,  and  that 
of  the  water  50°  F.,  what  would  be  the  final  temperature  (£)  of 
both? 

31.  If  coal  were  pure  carbon  it  would  take  2f  Ibs.  oxygen 
per  pound  of  coal  to  burn  it  to  carbon  dioxide  (C02).    If  air  con- 
tained 20  per  cent  by  weight  oxygen  and  80  per  cent  nitrogen, 


60  HEAT 

and  if  the  products  of  combustion  are  400°  F.  hotter  than  the  cold 
air  supply  when  they  go  up  chimney,  how  many  B.T.U  do  they 
carry  away? 

32.  If  50  per  cent  excess  of  air  is  supplied,  how  many  B.T.U. 
will  be  carried  awaylin  Problem  31? 

33.  If  the  heat  of  combustion  of  the  carbon  in  Problem  31  were 
entirely  used  to  heat  the  gaseous  products   (i.e.,   assuming  no 
losses   from    radiation,    conduction,    and    convection    during   the 
burning),   what   would   be   the   resulting   temperature   of   these 
products? 

34.  If  50  per  cent  of  air  were  used  in  Problem  33,  what  would 
have  been  the  resulting  temperature? 

35.  If  2.46  Ibs.  of  pure  oxygen  and  1  Ib.  of  acetylene  produce 
complete  combustion,   and  if  the  specific  heat   of  the  gaseous 
products  =  .240,  what  would  be  the  resulting  temperature  if  no 
heat  were  lost?    Assume  the  acetylene  and  the  oxygen  to  be  at  0°  C. 

36.  In  Problem  35,  find  the  resulting  temperature  if  the  neces- 
sary oxygen  is  supplied  from  air. 

NOTE.    Unless  otherwise  stated,  assume  23  per  cent  by  weight 
oxygen  and  77  per  cent  nitrogen  in  air. 

37.  One  pound  benzine  requires  2.46  Ibs.  of  oxygen  for  complete 
combustion.    What  is  the  highest  temperature  obtainable  with 
benzine  and  oxygen  under  the  same  assumptions  as  in  Problem  35? 

38.  Under  conditions  as  in  Problem  37,   what  temperature 
could  be  obtained  by  burning  benzine  and  air? 

39.  If  50  per  cent  excess  of  air  and  benzine  were  used  in 
Problem  37,  what  temperature  would  result? 

40.  How  many  cubic  feet  of  dry  air  at  32°  F.  will  1  Ib.  of  coal 
containing  14,000  B.T.U.  raise  40°  F.? 

(1  cu.ft.  air  weighs  .0817  Ib.) 

41.  A  room  12  X  16  X  8  originally  at  32°  F.,  has  burned  in   it 
1  cu.ft.  of  gas  giving  600  B.T.U.     If  escaping  air  is  at  the  same 
temperature    as  that  remaining  at  the  completion  of  the  com- 
bustion, find  temperature  of  air. 

42.  A  piece  of  fire-brick  weighing  2.83  Ibs.  is  to  be  used  to 
determine  a  furnace  temperature.     In  order  to  establish  its  average 
specific  heat  for  the  range  over  which  it  was  to  be  used,  it  was 
heated  in  an  oven  whose  temperature  was  known  to  be  1950°  F. 
and  then  dropped  into  19.8  Ibs.  water  at  40.6°  F.     If  the  resulting 
temperature  of  the  water  was  100.8°  F.,  find  the  specific  heat  of 
the  brick. 

(Water  equivalent    of   the  calorimeter,  stirrer,  thermometer, 
etc.,  was  .4  Ib.) 


III.      SPECIFIC  HEAT  AND  CALORIMETRY          61 

43.  If  for  every  pound  of  coal  burned  under  a  steam  boiler 
12  Ibs.  of  gaseous  products  go  up  the  flue  at  a  temperature  of 
600°  F.,  find  the  energy  carried  away  in  B.T.U.  if  the  boiler-room 
temperature  is  60°  F. 

(Assume  specific  heat  of  gas  to  be  .237.) 

44.  What  fractional  part  of  a  horse-power  hour  would  this 
energy  be  if  it  could  be  saved  and  made  to  do  useful  work? 

45.  If  2  Ibs.  of  steam  is  allowed  to  go  through  the  fire  along 
with  the  air  to  prevent  the  formation  of  too  large  masses  of  coke, 
how  much  additional  energy  is  taken  from  the  fire  by  the  steam 
if  air  escapes  up  the  flue  at  a  temperature  of  600°  F.? 

(Specific  heat  of  steam  .500.) 

46.  If  an  air-cooled  gasoline  engine  has  an  efficiency  of  20  per 
cent  it  is  clear  that  80  per  cent  of  the  energy  in  the  fuel  must  be 
either  carried  off  from  the  exhaust  or  " radiated"  from  the  cylinder. 
A  certain  engine  burns  24  Ibs.  of  liquid  fuel  per  hour,  containing 
19,500  B.T.U.  per  pound;  for  every  pound  of  fuel  19  Ibs.  of  air 
was  also  put  through  the  cylinder.     If  the  air  was  taken  in  at 
60°  F.,  and  the  temperature  of  the  exhaust  was  780°  F.,  how 
much  energy  passed  out  via  the  exhaust?     How  much  was  left 
to  be  radiated  off  per  hour  if  the  combustion  was  complete? 

(Assume  specific  heat  of  gases  in  exhaust  equal  to  .237.) 

47.  If  in  the  engine  referred  to  in  the  previous  problem,  60  per 
cent  of  the  energy  in  the  fuel  was  "radiated"  from  the  surface  of 
the  cylinders,  how  many  pounds  of  air  must  have  been  heated 
from  60°  F.  to  180°  F.  per  hour? 

(Specific  heat  of  air  .237.) 


62  HEAT 


SUMMARY,    CHAPTER   III 

THE  SPECIFIC  HEAT  of  a  substance  is  the  capacity 
of  a  unit  mass  of  the  substance  to  take  up  heat  energy. 
The  specific  heat  of  a  substance  is  the  quantity  of  heat 
energy  required  to  raise  a  unit  mass  one  degree. 

B.T.U.  added 
Sp.H.  = 


Sp.H.= 


Weight  in  pounds  X  rise  hi  temperature  hi  F.  deg. 

Calories  added 

Weight  hi  grams  X  rise  hi  temperature  hi  C.  deg. 


CALORIMETERS  are  instruments  with  which  quan- 
tity of  heat  energy  is  measured.  Calorimetry  is  the 
name  given  to  the  process  of  measuring  energy  with  a 
calorimeter. 

In  the  method  of  mixtures,  HEAT  EQUATIONS  are 
written  based  upon  the  assumption  that  no  energy 
is  lost  during  the  period  of  manipulation. 

1 I )  Heat  gained  =  heat  lost. 

(2)  Total  heat  before  mixing  =  total  heat  after  mixing. 
These  equations  with  only  slight  variation  apply 

to  other  methods. 

ACCURACY  in  calorimetry  depends  upon  careful 
attention  to  many  small  details,  such  as  accuracy  of 
thermometer  readings,  accuracy  of  weighings,  and 
corrections  for  water  equivalent,  radiation,  conduc- 
tion, convection,  and  evaporation. 


III.      SPECIFIC  HEAT  AND  CALORIMETRY          63 

THE  WATER  EQUIVALENT  is  usually  taken  as  ^  of 

the  weight  of  copper  calorimeters  and  represents  the 
amount  of  water  which  would  have  an  equivalent  capacity 
for  taking  up  heat. 

CORRECTIONS  for  radiation,  conduction,  and  con- 
vection may  be  avoided  in  many  cases  by  starting  with 
the  calorimeter  (and  contents)  as  far  below  room  tem- 
perature as  it  is  to  be  heated  above  room  temperature. 
Evaporation  may  be  neglected  in  most  cases  where 
the  water  is  below  40°  C. 


CHAPTER  IV 
EXPANSION 

28.  Expansion  of  Solids.  It  is  a  matter  of  common 
experience  that  in  general  when  bodies  are  heated  they 
expand.  Trolley  and  telegraph  wires  sag  noticeably  more 
in  summer  than  in  winter.  In  making  patterns  for  the  foun- 
dry an  allowance  must  be  made  for  the  contraction  of  the 
metal  when  it  cools  if  the  casting  is  to  be  made  an  exact 


FIG.  10. — Steam  Piping,  Showing  Method  of  Suspension. 

size.  Patternmakers  frequently  use  rules  too  long  by  J  in. 
to  the  foot.  Compensator  pendulums  are  placed  on  clocks 
and  compensated  balance  wheels  in  watches  to  correct  for 
the  effect  of  expansion.  The  amount  of  this  effect  varies 
for  each  substance  and,  if  the  texture  of  the  body  is  not 
uniform  in  all  parts  and  in  all  directions,  the  amount  of  the 
effect  may  vary  in  the  three  directions  in  the  body  itself. 

61 


IV.     EXPANSION 


65 


Thus  wood  has  a  much  greater  expansion  with  the  grain 
than  across  the  grain.  A  crystalline  substance  may  have 
a  different  rate  of  expansion  along  each  of  the  several  axes. 
The  effect  of  expansion  is  taken  into  consideration  in 
countless  practical  cases  where  it  is  not  necessary  to  make 
any  accurate  computation  of  the  amount  of  the  effect. 
Fig.  10  shows  the  steam  main  which  runs  along  the  ceiling 
of  the  Pratt  Institute  machine  shop  and  supplies  steam 


j 


FIG.  11. — Brooklyn  Bridge  Expan- 
sion Joint. 


FIG.  12. — Rail  Expan- 
sion Joint  on  Brook- 
.  lyn  Bridge. 


heat  to  the  electrical  laboratory  above.  It  will  be  seen 
that  this  piping  is  suspended  by  a  three-piece  strap  jointed 
at  A  and  B  so  that,  as  the  steam  changes  the  temperature 
of  the  iron  pipe,  expansion  can  take  place  without  injury 
to  the  supporting  straps  or  to  the  pipe. 


66 


HEAT 


In  Figs.  11,  12,  and  13  is  shown  an  expansion  joint  of 
the  Brooklyn  Bridge.  This  joint  is  intended  to  care  for  the 
expansion  due  to  the  stretching  under  varying  loads  as  well 
as  the  thermal  expansion.  It  will  be  noticed  from  Fig.  12 
(a  view  of  the  elevated  tracks  from  the  front  of  an  elevated 
train)  that  the  elevated  and  trolley  tracks  are  provided  with  a 
long,  wedge-shaped  lap  which  allows  for  a  relative  movement 
of  several  inches,  as  the  two  sections  slide  by  each  other. 
To  the  left  of  this  may  be  seen  the  break  in  the  third  rail. 

Fig.  13  shows  the  joint  as  seen  from  the  bridge  promenade. 


FIG.  13. — Expansion  Joint  on  Brooklyn  Bridge. 

S  telescopes  into  G  and  keeps  the  bridge  members  in  line. 
The  two  ends  of  the  bridge  section  M  and  N  are  supported 
by  the  suspension  cables  A  and  B.  Fig.  11  shows  this 
construction  more  clearly  as  the  casing  G  is  removed. 

While  in  the  majority  of  cases  where  an  allowance  is 
made  for  thermal  expansion  the  amount  is  so  small  that 
no  computation  is  attempted,  yet  it  may  be  accurately 
found,  if  desired. 

For  purposes  of  comparison  and  practical  computation 
it  is  convenient  to  know  the  increase  in  length  per  unit 


IV.      EXPANSION 


67 


length  per  degree,  and  a  table  at  the  back  of  the  book  gives 
a  number  of  these  rates  under  the  heading,  COEFFICIENT 
OF  LINEAR  EXPANSION. 

The  coefficient  of  linear  expansion  of  a  solid  = 

Increase  in  length 
Original  lengthXrise  in  temperature' 

This  quantity  is  usually  determined  for  the  range  of 
temperatures  from  freezing  to  boiling  of  water,  and  the 
average  value  given. 


FIG.  14. — Coefficient  of  Expansion  Apparatus. 

It  is  important  to  notice  that  the  unit  of  length  used 
appears  once  each  in  both  numerator  and  denominator  and 
therefore  does  'not  affect  the  numerical  value  of  the  coeffi- 
cient. But  the  unit  of  temperature  appears  only  in  the  de- 
nominator, and  therefore  there  is  a  different  numerical 
value  of  the  coefficient  for  each  temperature  scale  in  use. 
Accordingly  when  the  coefficient  is  stated  the  temperature 


68  HEAT 

unit  in  which  it  is  determined  must  also  be  stated.  Also 
if,  like  wood,  the  substance  has  more  than  one  linear 
expansion,  it  is  necessary  to  state  in  which  direction  the 
expansion  takes  place. 

In  Experiment  H  1-1,  the  coefficient  of  linear  expansion  is  deter- 
mined. Fig.  14  shows  the  apparatus,  which  consists  of  a  metal  rod 
soldered  into  an  outer  jacket,  A.  This  jacket  is  steam  heated  from 
the  steam  main  through  the  hose  B.  Hose  C  is  connected  to  the  drain 
pipe  so  that  the  water  that  is  condensed  in  the  jacket  A  will  be  allowed 
to  escape.  The  temperature  of  the  rod  is  read  from  the  thermometer 
T  before  the  steam  is  turned  on,  and  again  after  the  steam  has  heated 
the  rod  to  its  own  temperature.  The  increase  in  length  is  read  from 
the  micrometer,  M .  P  is  a  telephone  receiver  used  to  tell  when  the 
micrometer  makes  contact  with  the  metal. 

The  following  is  an  extract  from  the  laboratory  direc- 
tion sheets. 

Experiment  H  1-1.  Determination  of  the  Rate  of  Increase  in 
Length  of  a  Solid  on  Application  of  Heat. 

The  amount  of  increase  of  a  solid  for  ordinary  ranges  of  temperature 
is  very  slight.  Delicate  means  of  measurement  are  therefore  necessary. 
One  very  common  method  makes  use  of  a  micrometer  screw.  The 
metal  tested,  in  form  of  a  rod,  is  held  firmly  in  a  special  frame,  with 
one  end  pressed  tightly  against  a  stop.  A  micrometer  screw  is  mounted 
upon  the  frame  in  such  a  position  that  it  may  be  brought  in  contact 
with  the  other  end  of  the  rod. 

First  measure  the  length  of  the  rod  kt  room  temperature.  In 
doing  this  it  is  not  necessary  to  remove  the  rod  from  the  jacket. 
Take  jacket  and  all  from  the  support  and  place  it  on  the  desk  beside 
a  meter  stick.  Place  blocks  against  the  projecting  ends  of  the  rod 
and  against  the  meter  stick.  Read  positions  of  inside  edges  of  blocks. 

Record  the  reading  of  the  thermometer  in  the  jacket,  and  the 
reading  of  the  micrometer  when  in  contact  with  the  rod.  This  reading 
will  be  taken  by  turning  up  the  micrometer  until  a  click  is  heard 
in  the  telephone  receiver  shown  in  Fig.  14.  Turn  the  micrometer  screw 
back  a  fraction  of  a  turn  to  zero,  and  then  one  whole  turn  to  give  the 
rod  space  to  expand.  Do  this  carefully  so  that  you  will  be  able  to 
compute  accurately  the  difference  between  this  first  or  zero  reading 
and  the  second  reading  taken  when  hot. 

Then  connect  with  the  steam  main  and  pass  steam  through  the 


IV.     EXPANSION  69 

jacket    until    the    thermometer    ceases   to    rise.     Read   thermometer 
and  micrometer. 

The  following  is  a  set  of  data  obtained  from  one  of  these 
pieces  of  apparatus. 

DATA 

Kind  of  rod Aluminium 

Length  of  rod 24.5  ins. 

Temperature  of  rod  cold '. 21.0°  C. 

Micrometer  reading  cold 0273  in. 

Micrometer  turned  back  to  zero  and  then  one  whole  turn  1  0  ~ 

Temperature  of  rod  hot / 

Micrometer  reading  hot 0334  in. 

COMPUTATIONS 

Rise  in  temperature  of  rod 80.8°  C. 

Micrometer  was  turned  back 0273  +50=  .0773  in. 

Micrometer  was  advanced 0334  in. 

Elongation  of  rod =  .0773  -  .0344  =  .0439  in. 

.0439 

Elongation  per  inch =  =  .00179  in. 

.24.5 

Elongation  per  inch  per  degree  C = =  .0000221  in. 

80.8 

29.  Coefficient  of  Expansion  of  an  Area.  If  a  substance 
is  homogeneous  we  may  expect  a  surface  of  it  to  expand 
uniformly  both  in  length  and  in  breadth.  Its  increase  in  area 
may  be  computed  in  this  case  from  its  linear  coefficient.  A 
square  surface  having  unit  sides,  when  expanded  would  have 
each  side  increased  by  (at)  where  (a)  is  the  linear  coefficient 
and  (t)  the  rise  in  temperature.  The  expanded  length  of 
each  side  would  then  be  (1+at)  and  the  area,  (1+at)2. 

Removing  parentheses  we  have  area  =  l-f-2at+a2t2  and 
the  increase  in  area=2at+a2t2. 

For  most  computations  it  will  be  found  that  a2t2  is  a 
quantity  too  small  to  be  taken  into  consideration,  as  (a) 

is  usually  smaller  than   -.  and  therefore  a2  is  smaller 


70  HEAT 

than   iQQ  QQQ  QQQ-     Since  the  error  in   dropping  the  last 

term  is  practically  always  less  than  one  part  in  a  thousand, 
we  can  always  take  the  coefficient  of  twice  the  coefficient 
of  linear  expansion. 

The  coeffici  nt  of  areal  expansion  of  any  substance  = 

Increase  in  area 
Original  areaXrise  in  temperature  ' 

30.  Coefficient  of  Cubical  Expansion.  In  a  homoge- 
neous solid  we  can  compute  the  increase  in  volume  in  a 
similar  way  to  that  just  employed  to  compute  the  area  of 
a  face  of  the  solid.  In  this  case  let  us  assume  a  cube 
having  sides  of  unit  length. 

When  cold  the  volume  =  (I)3  =  1  ; 
If  expanded,  the  length  of  each  side  =  (1-f-at); 
and  the  volume  =  (1-fat)3. 

Removing  parentheses,  the  volume  ==l+3at-|-3a2t2-fa3t3. 
Subtracting  the  original  volume,  the  increase  in  volume 

=3at+3a2t2+a3t3. 


But  Sa^+a3!3  can  be  neglected  because  it  is  too 
small  to  be  significant.  Then  we  can  always  take  the 
coefficient  of  CUBICAL  EXPANSION  AS  THREE  TIMES  THE 
COEFFICIENT  OF  LINEAR  EXPANSION. 

The  Coef.  of  Cubic  Expansion  of  any  substance  = 

Increase  in  Volume 
Original  VolumeXRise  in  Temp.' 

In  tables  only  the  linear  coefficients  of  solids  are  given. 


IV.     EXPANSION  71 

These  tables  are  sometimes  made  out  to  show  expansion 
for  an  increase  in  temperature  of  1°  C.,  and  sometimes 
for  an  increase  in  temperature  of  1°  F.  Since  the  centigrade 
degree  represents  f  as  much  increase  hi  temperature  as  1° 
F.,  and  therefore  I  the  expansion,  to  change  a  Fahrenheit 
coefficient  to  a  centigrade  coefficient,  multiply  by  f .  The 
table  in  the  appendix  is  given  in  centigrade.  To  change  to 
the  Fahrenheit  coefficient,  it  will  be  necessary  to  multi- 
ply by  I. 

31.  Expansion  of  Liquids.  Cubical  expansion,  as  already 
denned,  takes  place  in  liquids.  This  quantity,  however, 
is  not  so  easily  determined  for  a  liquid  as  for  a  solid,  because 
it  is  always  necessary  to  correct  for  the  expansion  of  a  retain- 
ing vessel.  Thus,  if  a  liquid  such  as  water  is  contained  in 
a  vessel  of  glass,  the  vessel  may  increase  in  volume  either 
faster  or  slower  than  the  water  in  the  vessel.  So  apparently 
the  water  may  either  expand  or  contract. 

By  measuring  the  apparent  increase  in  volume  of  the 
liquid  in  the  vessel,  giving  it  a  minus  sign  if  it  is  a  contrac- 
tion, and  dividing  by  the  original  volume  and  the  rise  in 
temperature,  we  have  what  is  called  the  apparent  coefficient 
of  cubical  expansion.  The  apparent  cubical  coefficient  of 
expansion  of  the  liquid  added  to  the  cubical  coefficient  of  the 
vessel  will  give  the  absolute  coefficient  of  cubical  expansion 
of  the  liquid. 

The  Apparent  Coef.  of  Cu.  Expansion  of  a  Liquid  in  a  Vessel  = 

Apparent  Increase  in  Vol. 
Apparent  Original  Vol.XRise  in  Temp.' 

The  Apparent  Coef.  of  Cu.  Expansion-^- Coef.  of  Cu.  Expan- 
sion of  the  Vessel  =  Absolute  Cu.  Coef.  of  the  Liquid. 

This  is  a  correct  statement  to  just  the  same  degree  as  the  state- 
ment that  the  cubical  coefficient  of  expansion  is  3  times  the  linear 
coefficient.  It  should  also  be  remembered  that  these  coefficients  are 


72  HEAT 

always  an  average  value  over  a  specified  range  of  temperature. 
They  are  never  based  on  the  rate  of  expansion  at  a  fixed  or 
standard  temperature. 

Problem  1.  Two  trolley  poles  120  ft.  apart  are  strung  with 
copper  wire.  If  the  coldest  winter's  day  is  40°  F.  below  zero, 
and  if  the  thermometer  read  80°  F.  when  the  line  was  erected, 
how  much  will  it  draw  in  cold  weather?  (Disregard  its  elasticity 
and  allow  no* slack.) 

From  table: 

Coefficient  of  expansion  of  copper  in  centigrade  system,  .0000168 
Coefficient  in  Fahrenheit  system  will  be 

.0000168X1=  .00000933. 

If  1  ft.  expands  .00000933  ft.  in  a  rise  of  1°  F.,  120  ft.  will 
contract  120  X  .00000933=  .00011196  ft. 

If  cooled  1°  it  will  contract  an  equal  amount.  But  the  wire 
will  have  cooled  120°  F.  when  the  temperature  reaches  -  40°  F. 
Therefore  120  ft.  will  contract 

120 X. 0001 12  ft.  =.0134  ft.,  or  1.16  ins. 

Problem  2.  If  50-ft.  steel  rails  are  laid  when  the  temperature 
is  40°  F.,  how  much  space  must  be  left  between  each  pair,  assuming 
highest  summer  temperature  to  be  110°  F.?  (Disregard  the  elas- 
ticity of  the  steel.) 

From  table: 

Coefficient  of  expansion  for  steel  =  .0000123. 

(This  means  that  one  centimeter  of  steel  expands  .0000123 
of  a  centimeter  when  heated  1°  C.,  or  1  ft.  expands  .0000123  ft., 
or  1  in.  expands  .0000123  in.) 

To  reduce  to  Fahrenheit : 

.0000123X|=  .00000685. 

If  1  ft.  expands  .00000685  ft.  for  a  rise  of  1°  F.,  50  ft.  will 
expand  50  X. 00000685  ft.  =  .000343  ft. 

But  the  rise  in  temperature  is  110—40=  70°  F.,  therefore, 
50  ft.  wiU  expand  70  X. 000343  ft.  =  .0240  ft, 

.0240  ft.  =.288  in. 


IV.     EXPANSION  73 

Therefore  the  rails  should  be  laid  .288  inch  apart  to  avoid 
buckling  in  summer. 

Problem  3.  In  Problem  2,  what  would  have  been  the  force 
of  compression  in  the  rail  if  its  cross-sectional  area  was  4.2  sq.in., 
if  its  modulus  of  elasticity  was  24,000,000,  and  if  the  ends  of  the 
rails  were  riveted  together  at  the  temperature  stated  ? 

The  rail  was  compressed,   and  therefore  under  a  strain  of 


stress 

--  —  =  modulus. 

strain 

Let  x  =the  stress  (per  square  inch).    Then 
=  24000000, 


.00048 

z=24000000x.00048  =  11520  Ibs.  per  sq.in. 
Total  force  of  compression  =4.2  X 11520  =48400  Ibs. 

Problem  4.  A  full  glass  vessel  contains  400  gms.  of  mercury  at 
0°  C.  How  much  would  it  hold.'at  100°  C.? 

The  apparent  coef.  =  .000182 -3 X. 00000833. 

The  apparent  increase  in  volume  or  the  overflow  of  mercury 
=  (.000182 -.0000250)  X400xl00=6.28  gms. 

Therefore  there  will  remain  in  the  vessel  400  -6.28  =393.72  gms. 

Problem  5.  How  much  will  a  12-ft.  iron  boiler  tube  expand 
when  heated  from  40°  to  300°  F.? 

Problem  6.  How  much  will  a  300-ft.  span  of  a  steel  bridge  vary 
in  length  owing  to  the  change  from  a  summer  temperature  of  110° 
F.  to  a  winter  temperature  of  — 10°  F.? 

Problem  7.  Surveyor's  chain  66  ft. 'long  at  60°  F.  is  used  in 
zero  weather  to  measure  a  mile.  What  length  must  be  added  to 
a  measured  mile  to  have  a  true  mile? 

Problem  8.  What  change  takes  place  in  the  cubical  capacity 
of  a  glass  cylindrical  pendulum  bob  holding  10  c.c.  at  20°  C.  if 
heated  to  50°  C.? 

Problem  9.  A  steel  rod  1.64  ins.  in  diameter  is  to  be  used  to 
draw  the  walls  of  a  building  together.  If  the  rod  is  heated  to 
240°  F.,  what  tension  can  it  exert  in  cooling  to  75°  F.? 


74  HEAT 

Coefficient  of  expansion  of  steel  =  .000011, 
Coefficient  of  elasticity  of  steel  =  30,000,000. 
Problem  10.    A  steel  tie  of  8  sq.ins.  cross-section  area  is  to 
be  used  to  draw  the  bulging  walls  of  a  building  together.    When 
heated  up  to  400°,  the  ends  are  fastened  to  the  wall  and  the  rod  is 
allowed  to  cool  to  100°  F.    With  what  force  does  it  tend  to  draw 
the  building  together? 

32.  Expansion  of  Gases.  Gases,  being  fluid,  have  no 
definite  volume.  Unlike  liquids,  gases  have  an  extremely 
variable  volume. 

The  volume  of  a  gas  depends  among  other  things 
upon  the  pressure  upon  it.  Thus  1  Ib.  of  a  gas  such  as 
air  under  "standard  atmospheric  conditions,"  (under  760 
mm.  of  mercury  pressure  and  at  the  freezing  temperature 
of  water),  would  occupy  12.39  cu.ft.  If  kept  at  the  same 
temperature,  and  the  pressure  is  increased  by  168  Ibs.,  the 
volume  becomes  almost  exactly  1  cu.ft.  If  the  pressure 
were  allowed  to  drop  to  a  quarter  of  a  pound,  the  volume 
required  if  the  gas  were  kept  at  freezing  temperature  would 
be  approximately  182  cu.ft.  Whatever  the  volume  allotted 
to  the  pound  of  gas,  it  would  tend  to  expand  and  fill  it 
uniformly.  The  relation  that  exists  between  the  pressure 
and  the  volume  of  a  gas  kept  at  a  fixed  temperature,  is  expressed 
by  Boyle's  Law,  which  is : 

THE  PRESSURE  OF  A  GAS  VARIES  INVERSELY  AS  THE 
VOLUME  WHEN  THE  TEMPERATURE  REMAINS  CONSTANT. 

Keeping  in  mind  that  this  relation  holds  only  for  changes 
at  a  fixed  temperature,  this  may  be  more  briefly  written : 

PRESSURE X VOLUME  =  CONSTANT,  or  in  symbols: 

PXV= CONSTANT. 

When  a  gas  expands  (and  contraction  we  can  call  negative 
expansion)  according  to  Boyle's  law,  the  gas  is  said  to 
undergo  "  Isothermal  Expansion."  (See  also  p.  202,  sec- 
tion 69.) 

Distinct  from  isothermal  expansion  we  want  to  consider 


IV.     EXPANSION 


75 


the  expansion  of  gases  due  to  changes  in  temperature.  In 
order  that  we  may  keep  the  conditions  as  simple  as  possible, 
at  first  we  will  consider  only  changes  that  take  place  at 
constant  volume  or  at  constant  pressure. 

Suppose  then  that  we  were  to  take  1  Ib.  of  air  and  keep 
it  at  atmospheric  pressure  but  vary  its  temperature  and 
volume  in  suitable  apparatus.  The  resulting  data  plotted 
on  curve  paper  are  given  in  Fig.  15.  The  curve  is  a  straight 
line,  but  does  not  pass 
through  the  origin. 
From  this  we  see  that 
there  is  a  constant 
increase  in  volume  for 
each  rise  of  1°  C.  The 
volume  at  0°  C.  is  12.39 
cu.ft.,  and  the  volume 
increases  to  37.17  cu.ft. 
at  546°  C.  Thus  for 
a  rise  in  temperature 
of  546°  C.  an  increase 
in  volume  of  24.78  cu.ft. 
takes  place.  Originally 
at  0°  C.  there  was  12.39 

cu.ft.,  so  there  has  occurred  an  increase  of  2  cu.ft.  for 
each  cubic  foot  originally  at  0°  C.  The  rate  of  increase 

2  1 

per  cubic  foot  per  degree  would  therefore  be  ^  or  ~™. 


—  w 

—£32 

8 

-> 

H 

3 

Sir, 

/ 

/ 

/ 

/ 

_y 

/ 

t*lb 

A 

/       Relation  between 
Temperature  and  Volume 
with 
Pressure  Constant 
For  1  Lb.  Air 

/ 

/ 

160°        0°        160°       3203       480C 
Temperature  Centigrade 

FIG.  15. 


This  means  that  the  air  increases     o  (°r  0.00366)  its  volume 


at  0°  C.  for  every  rise  of  1°  C.  anywhere  on  the  scale.  This 
quantity  is  called  the  coefficient  of  expansion  of  a  gas  at 
constant  pressure. 

Exp.  H  1-2  discussed  on  p.  80  shows  how  this  quantity 
is  determined  in  the  laboratory. 

This  coefficient  is  a  cubical  coefficient,  since  it  is  a  coef- 
ficient of  change  of  volume,  and  therefore  in  any  experimental 


76  HEAT 

use  of  it  much  the  same  precautions  must  be  taken  as 
in  the  case  of  the  cubical  expansion  of  a  liquid.  However, 
this  difference  must  be  clearly  understood.  The  numerical 
value  of  the  coefficient  is  many  times  larger  than  the  coef- 
ficient for  a  liquid;  therefore  its  importance  in  computing 
gas  volumes  is  proportionately  increased.  Errors  must  be 
avoided  by  applying  more  exact  methods  of  computation. 
Accordingly  it  is  always  necessary  to  apply  the  coefficient 
to  the  volume  of  a  gas  at  0°  C.,  else  the  correction  will  be 
too  large  or  too  small,  according  to  the  initial  temperature. 
Thus  we  see  by  again  referring  to  the  curve,  Fig.  15,  that  1 

24.78 

Ib.  of  air  always  increases  —  -—  or  .0454  cu.ft.  per   degree. 

546 

Also   —  -   of  12.39  cu.ft.  =  .0454  cu.ft.     Now  if  we  take  —  - 

jj  /  o 


of  any  volume  above  0°  C.  we  get  a  quantity  larger  than 
.0454,  and  if  we  take  the  volume  for  any  temperature  below 
0°  C.,  we  get  less  than  .0454  cu.ft. 

This  same  coefficient  results  if  data  are  taken  and  plotted 
for  other  pressures  besides  that  used  in  plotting  Fig.  17. 
This  fact  is  usually  called  CHARLES'  LAW,  which  is  often 
stated  as  follows  : 

Tine  coefficient  of  expansion  of  a  perfect  gas  is  independent 
of  the  pressure  if  the  pressure  is  constant. 

Air,  nitrogen,  oxygen,  hydrogen,  and  a  few  other  gases 
obey  this  law  rather  closely. 

The  above  facts  may  be  set  forth  in  a  formula  of  typical 
form.  If  V*  =  the  volume  at  any  temperature,  t°  C., 
Vo  the  volume  at  0°  C.,  the  freezing-point  of  water,  and 
a  =  the  centigrade  coefficient  of  expansion,  then 

V,=V0(l+at). 

This  coefficient  worked   out  for  the  Fahrenheit  scale 

is  —  ,  and  care  must  always  be  taken  to  use,  as  the  basis 
493 


IV.     EXPANSION 


77 


for  computation,  the  volume  at  the  freezing-point  of  water. 
The  formula  has  the  same  form,  being  V«  =  V32(l+atO 
(whent'  =  t-32). 

33.  Pressure  Effects  Due  to  Change  of  Temperature  at 
a  Constant  Volume.  If  1  Ib.  of  a  perfect  gas  be  kept  at 
a  constant  volume  of  12.39  cu.ft.  and  its  temperature  varied, 
the  resulting  data  will  plot  into  a  curve  similar  to  that  in 
Fig.  16. 

It  will  be  seen  that  this  curve  closely  resembles  that 
of  Fig.  15. 

If  the  rate  of  increase  of  pressure  be  determined  by  finding 
the  slope  of  the  curve  we  find  that  again  we  get  the  fraction 

—  —  if  we  take  the  pressure  in  atmospheres.  In  this  case 
27  o 


we  can  again  take 


(or  .00366)   as  the  coefficient  of 


expansion  if  we  keep  in  mind  that  this  fraction  expresses  the 
increase  in  pressure  as 
a  fractional  part  of  the 
pressure  at  the  freezing- 
point  of  water. 

The  coefficient  of  ex- 
pansion of  a  gas  at 
constant  volume  is  the 
increase  in  pressure  per 
degree  rise  in  tempera- 
ture, divided  by  the 
pressure  at  freezing- 


ou 

/ 

jj 

floA 

V 

1 

/ 

/ 

z 

/  Relation  between 
Temperature  and  Pressure 
with 
Volume  Constant 
For  1  Lb.  Air 

/ 

/ 

160C 


160C 


Temperature  Centigrade 
FIG.  16. 


point  of  water. 

This  coefficient  is 
determined  in  Exp. 
H  1-3,  which  is  discussed  in  full  on  p.  86. 

Just  as  in  the  case  of  expansion  at  constant  volume,  care 
must  always  be  exercised  to  apply  the  coefficient  to  the  con- 
dition of  the  gas  at  freezing-point  of  water. 


78  HEAT 

The  equation  by  which  the  relation  between  the  pressure 
of  a  gas  at  constant  volume  and  varying  temperatures  is 
expressed,  follows: 

P,  =  Po(l+at); 
where 

P<=the  pressure  at  t°  centigrade; 

Po  =  the  pressure  at  0°  centigrade; 
and 

a  =  the  coefficient  of  expansion  at  constant  volume. 

Similarly,  the  equation  for  use  when  the  temperatures  are  in 
Fahrenheit  degrees  is 


where  t'=t—  s  or  the  amount  that  t  is  above  or  below  the  stand- 
ard temperature. 

It  will  be  noticed  that  this  expression  has  the  same  form 
as  V«=Vo(l+at)  and  is  also  like  the  equation  which  gives  the 
resistance  Rt  of  a  conductor  at  any  temperature  t  as  compared 
to  the  resistance  Rs  at  a  standard  temperature  s,  when  t' 
is  the  difference  between  t  and  s 

R/=R5(l+at'). 

All  of  these  formulae  are  applicable  whether  the  Fahren- 
heit or  centigrade  scale  is  used,  provided  a  proper  coefficient 
is  taken. 

The  use  of  these  formulae  is  illustrated  by  the  set-off  prob- 
lems at  the  end  of  the  next  section. 

Problem  11.  If  3.5  Ibs.  of  nitrogen  has  a  volume  of  43.8  cu.ft. 
at  0°  C.,  what  is  its  volume  at  20°  C.? 


IV.     EXPANSION  79 

F20 


T  r  try    o  \  / 

(273)' 
F20  =  47.0  cu.ft. 

Problem  12.  If  72  cu.ft.  of  oxygen  at  25°  C.,  is  heated  to  100° 
C.,  what  will  be  its  new  volume?  This  should  be  done  in  two 
steps.  First : 

F,=  V0(l+at), 


(298) 


Fo  =  66. 
Second: 

Vt=  Fo(l-f-aO, 


T7  «A 

F10o°=66--, 

Fioo°  =  90.2  cu.ft. 

Problem  13.  A  sealed  vessel  contains  air  at  20°  C.  and  at 
atmospheric  pressure.  If  it  is  heated  to  1200°  C.  without  change 
of  volume,  what  would  be  the  resulting  pressure? 

As  in  the  example  above,  we  will  do  this  in  two  steps,  first: 


14.7- Pol  1+ 


2T3X2°)' 


80  HEAT 

Po  =  13.7, 

Pi2oo=  !3.7n  +  ~jXi2ooY 

Pi200  =  74.0  Ibs. 

This  example  may  be  done  in  one  step  by  first  combining  the 
formulae  as  follows: 


let 
and 
then 
and 

Transposing 

Substituting 


ti  =  the  initial  temperature, 
tz  =  the  final  temperature, 
Pit -Pott +«&'), 


Pn 


1+ati      1  +  at2 
14.7 


Pl200 


20  1200' 

"^273          ^273 

14.7X273X1473 
293X273 


=  74.0  Ibs. 


Problem  14.    If  200  cu.cms.  of  hydrogen  at  75°  F.  were  cooled 
to  freezing,  what  volume  would  result? 


Remember  that  VQ  =  pressure  at  freezing  and  t'  is  the  difference 
between  the  freezing  temperature  and  t. 

200=  ^(i+JSj 
F32°  =  184  cu.ft. 

Problem  15.  If  500  c.c.  of  a  perfect  gas  is  taken  at  atmospheric 
pressure  and  600°  F.  and  cooled  to  freezing,  what  volume  will 
it  have? 


IV.     EXPANSION  81 

Problem  16.  If  500  c.c.  of  a  perfect  gas  were  taken  at  300°  C. 
and  atmospheric  pressure,  what  would  be  its  pressure  at  0°  C.? 

Problem  17.  If  60  cu.ft.  of  a  perfect  gas  is  cooled  from  a  tem- 
perature of  100°  C.  to  20°  C.,  what  will  its  final  volume  be? 

Problem  18.  If  a  perfect  gas  were  heated  from  72°  F.  and  15 
Ibs.  pressure,  to  1600°  F.,  and  if  the  volume  were  kept  constant, 
what  pressure  would  result? 

34.  Absolute  Temperature.      Inspection    of    the    curve 
of  Figs.  15  and  16  shows  an  important  fact.     If 'projected 
backward  to  the  X  axis  they  seem  to  cut  it  at  —273°  C. 
(or  at  —461°  F.)..    Apparently,  if  we  were  to  continue  to 
reduce  the  temperature,  the  volume  in  one  case  and  the  pres- 
sure in  the  other  would  be  entirely  eliminated,  and  we  would 
have  arrived  at  a  state  of  affairs  beyond  which  we  could  not 
well  go. 

If,  then,  this  is  the  lowest  temperature  that  could  exist, 
it  is  logical  to  take  it  as  the  zero  of  our  temperature  scales. 
Scales  using  this  point  as  zero  are  called  absolute  scales. 
The  absolute  centigrade  scale  uses  this  point  and  the  centi- 
grade degree,  so  that  temperatures  on  it  are  273°  more  than 
on  the  centigrade  scale. 

The  absolute  Fahrenheit  scale  similarly  uses  the  Fahren- 
heit degree,  and  temperatures  on  it  are  461°  more  than  on 
the  Fahrenheit  scale.  Thus  boiling  of  water  takes  place 
at  373°  absolute  centigrade  and  at  673°  absolute  Fahren- 
heit. 

35.  Expansion  with  Three  Variables.      If     the    curves 
of  Figs.   15  and   16  were  to  be  replotted,  using  absolute 
temperatures,  we  would  have  the  curve  in  each  case  going 
through  the  origins.     This  shows  that  in  the  case  of  expan- 
sion at  constant  volume,  the  pressure  is  in  direct  proportion 
to  the  absolute  temperature.     Also  if  expansion  takes  place 
at  constant  pressure,  the  volume  is  in  proportion  to  the 
absolute  temperature. 

If  T  =  absolute  temperature,  we  may  express  this  in 
symbols  thus; 


82  HEAT 

VocT  where  pressure  is  constant,  and  V  =  volume. 

P  oc  T  where  V  is  constant  and  P  =  pressure, 
or 
V 
=  =  a  constant  when  P  is  constant. 

and 

p 

=  =  a  constant  when  V  is  constant. 

If  the  data  in  Figs.   15  and   16  when    replotted  gave 
straight-line  relations,  the  following  ratios  also  hold: 


also 


=       or       = 

Ti     T2  V2    To' 


P,_P2  Pl_Tl 

Ti     T2  P2    T2' 


From  these  statements  it  follows  that 

PV 

-=r  =  a  constant, 

and 

PV    PiVi     P2V2    P3V3 


T        Ti         T2        T3 


,  etc. 


The  same  conclusions  may  be  reached  from  the  following: 
From  pages  76  and  78  we  have: 

Va=Vo(l+ati), 
and 

V,2=Vo(l+at2). 

Dividing  these  two  equations, 

Va_Vo(l+ati) 
Vn     V0(l+at2) 

_l+att 
~l+at2' 


IV.    EXPANSION  83 


But  in  both  cases  a  =  — — . 

Substituting  we  have, 

ti_     273 +tt 

Va_       273        273        273 +ti 
V2  ~         t2  ~273+t2~273+t2' 
273        273 

But  273 +ti  =  absolute  temp.  Ti, 

and 

273 +t*  =  absolute  temp.  T2. 


=         and         =         or    ViT.-V.TL       ...     (I) 

Vf2        I  2  V2        12 


Similarly, 


By  Boyle's  Law 

PiVt=P2V2  .........     (Ill) 

If  we  multiply  Eqs.  I,  II  and  III  together 

P1V1V1T2P1T2  =P2V2V2T1P2T1, 

P12V12T22=P22V22Tl2. 

Taking  the  square  root 

P1V1T2  =  P2V2Ti, 
or 

P,V,     P2V, 

^7"TT'.  '  -fl  • 

or 


36.  Experiments  on  the  Coefficient  of  Expansion  of  Air. 
A.—  RELATION  OF  V  TO  T  WHERE  P  IS  CONSTANT 

Fig.  13  illustrates  a  piece  of  apparatus  used  to  determine  the  coeffi- 
cient of  expansion  of  air  at  constant  pressure.     The  U-tube  shown  has 


84 


HEAT 


2  — 


a  closed  graduated  arm  4,  and  into  the  open  arm  a  glass  tube  or  rod 
P  is  inserted  as  a  plunger.  The  bend  in  the  tube  is  filled  with  sul- 
phuric acid  S,  which  keeps  the  gas  in  A  dry  and  separates  it  from 
the  atmosphere.  The  acid  is  kept  at  the  same  level  on  both  sides 
by  raising  or  lowering  P. 

The  temperature  of  the  air  or  other  gas  inclosed  in  arm  A  is  varied 
by  placing  the  U-tube  in  a  bath  consisting  of  a  jar  of  water  or  oil. 

The  following  is  an  extract  from  the 
laboratory  direction  sheets  for  this  experi- 
ment. 

Experiment  H  1-2.  Coefficient  of  Expan- 
sion of  a  Gas  at  Constant  Pressure. 

Insert  the  bend  of  the  tube  in  the  jar  and 
surround  it  with  enough  cold  water  (about 
5°  C.)  to  completely  cover  the  short  arm. 
Hang  a  thermometer  in  the  jar  beside  the 
tube.  Stir  the  water  frequently,  and  allow 
the  apparatus  to  stand  until  the  enclosed  gas 
has  had  time  to  take  the  temperature  of  the 
water.  Then  adjust  the  plunger  in  the  sul- 
phuric acid  until  the  level  of  the  acid  is  the 
same  in  both  arms. 

Caution.  Do  not  break  the  tube  or  spill  any 
acid  upon  the  person  or  clothing,  as  it  is  con- 
centrated sulphuric  acid. 

Record  the  volume  of  air  and  the  ther- 
mometer reading. 

Connect  to  the  steam  main  and  pass  steam 
into  the  heating  coil  until  the  temperature 
of  the  water  has  been  raised  about  10°,  and 
repeat  the  operations  above.  Take  in  this 
manner  a  series  of  readings  of  temperatures 
and  volumes  of  gas  at  approximately  equal 
intervals,  until  as  high  a  temperature  as 

practicable  (about  80°  C.)  has  been  reached.  For  the  higher  tem- 
peratures, great  care  should  be  taken  to  adjust  the  levels  of  acid 
columns  and  read  the  volume  just  on  the  instant  of  reading  the 
thermometer. 

From  the  values  obtained,  plot  a  curve  showing  the  change  of 
volume  of  the  gas  with  temperature,  pressure  being  kept  constant. 
Use  temperatures  as  abscissae  and  plot  from  0°  C.  (The  bore  of  the 
tube  being  uniform,  the  length  of  gas  column  may  be  taken  as  repre- 
senting its  volume.)  This  curve  should  be  a  smooth  line  so  passing 


FIG.  17. 


IV.     EXPANSION 


85 


between  the  points  as  to  correct  for  experimental  errors  and  show 
probable  law  of  expansion  as  found. 

Extend  your  curve  backward  until  it  cuts  the  Y  axis,  thus  obtaining 
volume  at  0°  C. 

Selecting  a  volume  from  your   curve  for  some   convenient   even 
temperature,    preferably   as    high  as    possible,   compute    the    appar- 
ent coefficient  of  expansion 
of    the     gas     at     constant 
pressure  from  the  equation 
Vt=Vo(l+at).     For  V0  use 
value  obtained  by  curve. 

The  absolute  coefficient 
of  expansion  at  constant 
pressure  equals  a  plus  the 
coefficient  of  expansion 
(cubical)  of  glass. 

Using  "  absolute  tem- 
peratures" as  abscissae,  and 
starting  from  "  absolute 
zero"  as  the  origin,  re-plot 
your  readings.  Continue 
the  curve  backward.  At 
what  temperature  does  it 
cut  the  X  axis? 

The  curves  in  Fig.  18  are 
plotted  from  a  set  of  data 
taken  from  this  apparatus. 

Substituting  in  the  equations  as  directed, 

V9o.3=  V0(l+90.3a), 


52 


Relation  between 
Temp,  and  Volume 

with 
Pressure  Constant 


20         40         GO         80         100 

Temp.  Centigrade 
64        128       192       256        320 
Temp.  Centigrade  Absolute 

FIG.  18. 


384B 


5.25=  3.94(1+  90.3a), 
1.31  1 


a  = 


90.3X3.94      272 


.00368. 


No  correction  has  been  applied  for  the  expansion  of  glass.  Such 
a  correction  is  hardly  necessary,  since  there  are  large  errors  possible 
in  plotting  to  so  small  a  scale,  as  well  as  in  reading  the  volumes, 
correcting  for  difference  of  pressure,  etc. 

However,  such  a  correction  is  here  made  to  illustrate  the  method. 


Cubical  coefficient  of  glass  =  3  X  .0000087. 


86  HEAT 

The  increase  per  unit  volume  for  90.3°  C.  would  therefore 

=  90.3X3X.0000087, 
and  for  a  volume  of  5.25  the  increase  would 

=  5.25  X90.3X3X.  0000087, 
=  .0123. 

This  correction  is  the  largest  one  to  be  applied  to  any  of  the 
readings  and  represents  a  difference  of  f  of  the  smallest  scale  division 
in  reading  the  volume.  Clearly  it  is  smaller  than  the  average  error 
in  reading  the  volumes  off  the  tube  and  in  correcting  for  pressure. 

Curve  B  is  obtained  by  replotting  the  data,  using  absolute  tem- 
perature. The  curve  passes  very  near  the  absolute  zero. 

B.— RELATION  OF  P  TO  T  WHERE  V  IS  CONSTANT 

Fig.  19  is  a  photograph  of  a  piece  of  the  apparatus  used  to  deter- 
mine the  coefficient  of  expansion  of  air  at  constant  volume.  It  may 
very  properly  be  called  an  air  thermometer.  The  air  thermometer 
bulb  A  contains  dry  air  and  is  mounted  upon  the  same  upright  frame 
that  is  used  for  the  verification  of  Boyle's  law.  This  upright,  B,  carries 
a  sliding  scale,  C,  which  is  graduated  to  read  directly  in  pounds  per 
square  inch  when  mercury  is  used  in  the  adjustable  open  tube,  Z). 

The  atmospheric  pressure  is  determined  from  the  reading  of  the 
barometer  and  corrected  in  the  manner  explained  in  the  chapter  on 
instruments  under  "  Barometer  Corrections."  A  pointer  P2  (not 
shown  in  photograph)  is  placed  on  the  scale  C  at  the  corrected  value 
of  the  atmospheric  pressure.  This  pointer  is  not  moved  thereafter, 
but  the  whole  scale  is  moved  up  or  down  and  the  pointer  P2  kept 
exactly  opposite  R,  the  top  of  the  mercury  column  in  the  open  tube. 
Pi  is  fixed  to  M  and  the  mercury  in  the  closed  side  is  kept  exactly 
opposite  this  pointer,  while  the  reading  is  being  taken  on  the  scale 
C  at  a  point  directly  under  the  upper  edge  of  P. 

The  following  extracts  are  from  the  laboratory  direction  sheets 
for  the  use  of  this  apparatus. 

Experiment  H  1-3.  Increase  of  Pressure  of  Gas  at  Constant 
Volume  when  the  Temperature  is  Increased. 

Hang  a  thermometer  on  a  hook  in  the  upright  support  between 
the  mercury  columns  and  place  a  second  marker  P%  on  the  sliding 
scale  C. 


IV.      EXPANSION 


87 


Adjust  the  open  tube  so  that  the  mercury  in  the  closed  tube  is 
opposite  the  mark  M  and  the  marker  PI,  adjust  the  slider  C  until  pointer 
P2,  which  must  be  kept  set  at  the  corrected  atmospheric  pressure,  is  opposite 
R,  the  top  of  the  mercury  column  in  the  open  tube.  Read  the  pressure 
in  the  air  thermometer  bulb  on  scale  C  opposite  Pi.  Record  this 
pressure  and  thermometer  reading.  Then  lower  the  open  arm  several 
millimeters,  surround  the  air  bulb  with  cracked  ice  and  reduce  the 
temperature  of  the  air 
to  0°.  As  the  gas  con- 
tracts, its  pressure  will 
decrease  and  the  mer- 
cury will  rise  in  the  stem 
of  the  air  thermometer. 
This  must  be  watched 
carefully  and  the  open 
arm  lowered  as  con- 
traction occurs,  so  as  to 
keep  the  mercury  in  the 
stem  somewhat  below 
the  fixed  mark. 

Mercury  must  not  be 
allowed  to  pass  over  into 
the  bulb. 

When  the  tempera- 
ture has  fallen  to  0°  C., 
as  indicated  by  the  fact 
that  no  further  changes 
occur  in  the  position  of 
the  mercury  column,  ad- 
just the  open  tube  and 
the  sliding  scale  and 
record  the  pressure  in  the 
bulb  and  the  tempera- 
ture -indicated  by  the 
thermometer. 

Remove  the  ice,  put 
on  the  top,  and  run  a 

pipe  from  the  steam  main  to  the  bottom  of  the  vessel  surrounding 
the  air  thermometer  bulb.  See  that  this  is  about  f  full  of  water. 
Turn  on  the  steam  and  let  it  bubble  up  through  the  witer,  thus 
surrounding  the  bulb  with  steam. 

Watch  the  height  of  mercury  in  the  stem,  and  raise  the  vessel 
of  mercury  as  needed  to  keep  the  mercury  in  the  stem  about  at  the 


FIG.  19.— Air  Thermometer. 


88  HEAT 

mark.  When  a  constant  temperature  has  been  reached,  set  the 
mercury  exactly  at  the  mark,  and  record  as  before  the  pressure  of  the 
air  in  bulb  and  the  temperature  on  the  suspended  thermometer  out- 
side and  also  the  thermometer  in  the  steam. 

N.B.  Lower  the  open  tube  before  removing  the  steam  jacket. 

Compute  the  temperature  of  the  steam  from  the  barometer  reading. 

From  your  data,  compute  the  increase  of  pressure  per  degree  C. 
Compare  this  with  the  pressure  at  0°  C.  The  ratio  of  increase  of 
pressure  per  degree,  to  pressure  at  zero  =  the  coefficient  of  increase 
of  pressure  at  constant  volume.  (The  increase  in  capacity  of  the 
bulb  is  here  so  slight  in  comparison  with  the  increase  of  pressure  that 
it  is  neglected  as  being  well  within  the  limits  of  accuracy  of  the 
method,  and  volume  of  gas  is  taken  as  constant  when  kept  at  the  mark 
at  the  stem.) 

Express  your  coefficient  both  as  a  fraction  having  a  numerator 
of  one  and  as  a  decimal.  Assuming  the  coefficient,  from  your  values 
of  pressure  at  0°  C.,  and  room  temperature,  compute  room  tem- 
perature and  compare  with  thermometer  reading.  This  illustrates  a 
method  of  measuring  temperatures  by  an  air  thermometer.  With 
porcelain  bulbs  high  temperatures  may  be  thus  measured. 

The  following  data  were  taken  according  to  these  direc- 
tions. 

DATA 

Barometer  reading 14.48  Ibs. 

"        corrected  748.4  mm 14.43  Ibs.  per  sq.in. 

Temperature  of  apparatus 23.4°  C. 


^  Reading  of  pressure 15.42  Ibs. 

With  ice  about  bulb 

Temperature  of  apparatus 23.2°  C. 

Reading  of  pressure 14.18  Ibs. 

(  Temperature  of  apparatus 23.8°  C. 

I  Reading  of  pressure 19.36  Ibs. 

COMPUTATIONS 

In  reading  2,  the  mercury  on  both  sides  was  so  nearly  level  that 
no  correction  need  be  made. 

In  reading  3,  the  pressure  in  the  bulb  differs  from  that  outside 
by  19.36 -14.43  =  4.93  Ibs. 

Taking  the  cubical  coefficient  of  expansion  of  mercury  as  .000182, 
the  true  excess  over  the  atmospheric  pressure  Pgo.G  is  given  by  the 
following  equations: 


IV.     EXPANSION  89 

4.93=  P99-6(l+  23.8  X. 000182), 
P99.6  =  4.91  Ibs. 

This  result  is  .02  Ib.  lower  than  that  obtained  without  the  cor- 
rection, showing  that  the  pressure  as  read  was  .02  Ib.  too  high. 

True  pressure  at  99.6°  C.  =  19.34  Ibs. 

True  expansion  from  0°  C.  to  99.6°  C.  =  19.34-14.18  =  5.16. 
Expansion  per  degree  centigrade,  .0518. 

Expansion  per  degree  =    1 
Pressure  at  0°  C.          274 

(  From  these  experimenjs^it  will  be  seen  that  the  coef- 
ficient of  expansion-alTconstant  volume  may  be  found  by 
noting  the  increase  in  pressure  between  any  two  temper- 
atures and  dividing  this  by  the  increase  in  temperature 
and  by  the  computed  pressure  at  0°  C.  The  coefficient 
of  expansion  at  constant  pressure  may  be  found  similarly. 
By  this  method  the  coefficient  of  expansion  of  gases,  which 
would  condense  to  the  liquid  state  or  even  become  solid 
if  cooled  to  zero,  centigrade,  are  found  and  referred  to 
standard  conditions.  However,  the  coefficient  of  expansion 
so  determined  is  not  constant  for  any  given  gas,  and  its 
value  will  depend  upon  the  range  of  temperatures  over 
which  it  has  been  determined.  This  temperature  range 
should  always  be  stated  with  the  coefficient,  for  the  coefficient 
to  have  any  accurate  meaning. 

The  coefficient  of  expansion  of  a  gas  as  just  defined  applies 
only  to  a  so-called  perfect  gas;  that  is,  a  gas  that  obeys 
Boyle's  and  Charles'  laws.  Since  there  is  no  gas  that  obeys 
these  laws  we  must  not  expect  the  coefficients  to  be  exactly 
equal  to  the  theoretical  value  given.  In  the  case  of  any 
particular  gas  the  coefficient  of  expansion  at  constant 
pressure,  and  the  coefficient  of  expansion  at  constant 
volume  will  both  differ  from  the  theoretical  value  and  from 
one  another. 


90  HEAT 

By  assuming  that  you  know  the  constants  of  the  appara- 
tus used  in  Experiment  31-3,  the  piece  may  be  used  as  a 
thermometer.  A  refined  type  of  this  thermometer,  known 
as  the  standard  air  (hydrogen  and  nitrogen  have  also  been 
used)  thermometer,  is  regularly  used  to  calibrate  and  correct 
very  accurate  mercury  thermometers. 

37.  Expansion  of  Gases.  Boyle's  and  Charles'  laws. 
In  Section  41,  Boyle's  and  Charles'  laws  were  combined 
in  the  following  formulae: 

PV  PV    PiVi    P2V2 

-7p-  =  constant,     and    -^-  =  -^—  =  -7^—  =  etc., 

where  P  is  pressure,  V  is  volume,  and  T  is  absolute  temper- 
ature. 

"  R  "  is  often  used  for  this  constant  when  the  formula 
is  applied  to  one  pound  of  air,  and  the  formula  is  then 
written: 

PV=RT. 

Since  1  Ib.  of  air  at  14.7  Ibs.  per  sq.in.  pressure  occu- 
pies about  12.4  cu.ft.  at  32°  F.  or  493°  absolute  Fahrenheit, 
for  air 

14.7X12.4 
~493~ 

For  any  weight  of  air  in  pounds  the  formula  is  : 


This  formula  is  very  frequently  used  with  the  value 
.37  for  mixtures  of  gases  other  than  air.  In  gas-engine 
problems,  for  example,  R  =  .37  gives  results  as  accurate  as 
the  nature  of  the  problems  requires. 

Sometimes  P  is  expressed  in  Ibs.  per  sq.ft.,  in  which 
case  the  pressure  is  numerically  144  times  larger  and 
R  =  .37  X  144  =  53.  See  section  68,  Chapter  VIII. 


IV.     EXPANSION  91 

By  using  this  expression,  one  may  briefly  and  quickly 
solve  many  practical  problems  which  would  require  many 
steps  if  worked  by  the  formulae  containing  the  coefficient 
of  expansion.  One  cannot  investigate  in  a  quantitative 
way  what  takes  place  in  the  cylinder  of  an  air  compressor, 
of  an  explosion  engine,  or  of  a  steam  engine  without  its 
use. 

A  few  simple  problems  will  be  given  here  in  advance 
of  the  chapters  on  "  Steam  Power  Plants/'  and  "  Gas  Power 
Plants,"  to  illustrate  the  use  of  the  above  formula. 

In  order  to  express  these  problems  in  the  usual  technical  language 
the  following  terms  are  used: 

THE  STROKE  of  an  engine  is  the  linear  distance  along  the  cylinder 
swept  through  by  the  piston. 

That  part  of  the  total  volume  at  each  end  of  the  cylinder  not 
swept  through  by  the  piston  is  called  the  CLEARANCE.  Clearance 
is  necessary  for  several  practical  reasons,  one  of  which  is  to  prevent 
pounding  due  to  the  compression  of  any  small  amount  of  liquid  and 
of  the  usual  amount  of  gases  left  in  the  cylinder  after  exhaust  takes 
place. 

The  BORE  of  an  engine  is  the  diameter  of  its  cylinder. 

Problem  19.  An  air  compressor  pumps  100  cu.ft.  of  free  air 
per  minute  from  a  room  of  average  temperature  of  78°  F.  What 
is  the  weight  of  air  pumped?  (Neglect  effect  of  moisture.) 

14.7  normal  atmospheric  pressure. 
F=  100  cu.ft., 
T=  461+78=  539, 
PV      14.7X100 


=  .37JF, 

J.  OOtf 

i  ±  7  v  1  nn 
W  = 


53937         '- 

Problem  20.    The  air  in  Problem  19  is  conveyed  to  a  rock  drill 
at  100  Ibs.  per  square  inch  pressure,  and  before  being  used  is 


92  HEAT 

preheated  to  400°  F.    What  volume  of  compressed  air  is  used 
by  the  rock  drill? 


14.7  X  100  _  100F2 
539  861    ' 

72=20.0cu.ft. 

Problem  21.  A  gas  engine  having  20  per  cent  clearance 
draws  a  charge  at  14.7  Ibs.  pressure  and  70°  F.  If,  when  the 
charge  is  compressed  into  the  clearance,  the  pressure  is  160  Ibs., 
what  is  the  temperature?  Assume  that  the  charge  fills  both  the 
clearance  and  the  volume  displaced  by  the  cylinder. 

PiFx     P2F2 


V\  =  120  per  cent  of  the  stroke  X  piston  area,  since  gas 
is  drawn  into  both  the  clearance  volume  and  the  volume  dis- 
placed by  the  piston  as  it  makes  its  stroke. 

F2  =  20  per  cent  of  the  stroke  X  piston  area,  as  the  piston 
compresses  all  the  gases  into  the  clearance  volume,  which  is  stated 
to  be  20  per  cent. 

Pi  =  14.7,  , 

P2=  160, 

T^  461  +70  =  531. 
Then 

14.7X120       160X20 


531  Tz 

160X20X531 
14.7X120      ' 

Tz  =  963  absolute, 
or  502°  F. 


IV.     EXPANSION  93 

Problem  22.  In  Problem  21,  after  the  charge  is  fired  the  tem- 
perature becomes  3258°  F.  What  was  pressure  then? 

If  we  assume  that  the  piston  has  not  moved  from  its  position, 
in  the  previous  problem  the  volume  remains  the  same  as  before 
and  so  F2  =  F3. 


14.7  X  120  _P320 
531  J     ~3719' 

P3  =  560.7  Ibs.  absolute, 

or,  546  Ibs.  per  square  inch  in  excess  of  atmosphere. 

Problem  23.  In  Problem  21,  at  the  end  of  the  expansion  stroke, 
the  pressure  becomes  40  Ibs.  What  was  the  temperature? 

PiF1_P2F2_P373_P4F4 
T,   "      T2   "      T>   "      T<  ' 

14.7  X  120     40  X  120 

531  ~  T<      ' 

r4  =  1445  absolute, 

or  984°  F. 

Problem  24.   1000  cu.ft.  of  free  air  at  72°  F.  weighs  how  much? 

Problem  25.  If  compressed  to  120  Ibs.  per  square  inch,  and 
cooled  to  72°  F.,  what  volume  would  the  air  in  Problem  24  occupy? 

Problem  26.  At  a  temperature  of  500°  F.,  what  volume  would 
it  occupy  if  under  120  Ibs.  pressure? 

Problem  27.  An  automobile  tire  is  pumped  up  to  80  Ibs.  per 
square  inch  at  a  temperature  of  80°  F.  If  it  would  burst  at 
100  Ibs.  pressure,  how  hot  must  it  get  before  bursting?  Assume 
that  the  volume  of  air  in  the  tube  does  not  change. 

Problem  28.  Solid  C02  gives  a  temperature  of  —  80°  C. 
If  a  glass  bulb  were  sealed  off  while  it  was  cooled  to  this  temp- 
erature, what  pressure  would  result  inside  the  bulb  if  it  contained 
air  and  was  heated  to  a  room  temperature  of  25°  C.  Assume 
that  no  change  in  volume  takes  place  in  the  bulb. 

Problem  29.  If  this  glass  bulb  has  a  volume  of  1000  c.c.  at 
25°  C.,  what  weight  of  air  does  it  contain? 

Problem  30.  What  is  R  for  C02  in  the  expression  PF  =  RT 
if  under  standard  conditions  1  cu.ft.  of  C02  weighs  ,07704  lb.? 


94  HEAT 

Problem  31.  A  gas  engine  having  25  per  cent  clearance  draws 
a  charge  at  14.7  Ibs.  pressure  and  60°  F.  If  when  the  charge  is 
compressed  into  the  clearance  the  pressure  is  141.1  Ibs.,  what  is 
the  temperature? 

Problem  32.  In  Problem  31  after  the  charge  is  fired  the  tem- 
perature becomes  4258°  F.  What  was  pressure  then? 

Problem  33.  In  Problem  31,  at  end  of  expansion  stroke,  the 
pressure  becomes  69.4  Ibs.  What  was  the  temperature? 

Problem  34.  A  charge  of  .14  Ib.  of  gas  and  air  was  drawn  into 
a  cylinder  having  .8  in.  clearance,  8  ins.  stroke,  and  10  ins.  diameter. 
Combustion  temperature  =  4000°  F.  After  expansion,  tempera- 
ture was  reduced  to  2000°  F. 

What  was  pressure  at  explosion? 

What  was  pressure  at  end  of  expansion? 

38.  Density   and   Volume   Affected   by  Expansion.    A 

solid  cube  of  a  given  material,  having  unit  dimensions  at 
0°  C.,  may  have  a  density  as  given  in  the  table  for  such  a 
substance,  but  clearly  if  it  is  heated  to  t°  C.,  its  volume 
will  have  changed  though  its  weight  will  remain  the  same.  If 
its  original  weight  at  0°  C.=Wo  and  its  volume  =  1,  its  new 
volume  will  be  l+3at  when  a  is  its  linear  coefficient  of 
expansion. 

As  Wo  is  really  the  weight  per  unit  volume  or  the  density 
at  0°  C.,  the  density  at  t°  C.  will  be  different.  If  WT  equals 
the  density  at  T°  C.,  we  may  write  its  value  as, 

Wo 


l+3at'j 

a  quantity  which  is  clearly  smaller  than  Wo  when  a  and  T 
are  positive. 

Tables  of  densities  of  materials  should  accordingly  be  used 
with  care  when  the  materials  are  at  a  temperature  varying 
considerably  from  the  normal,  or  from  that  at  which  the  den- 
sities were  determined.  The  correct  density  may  be  obtained 
by  first  finding  the  change  in  volume  that  would  take  place 
during  the  change  of  temperature  from  that  mentioned  in 


IV.     EXPANSION  95 

the  table  to  the  temperature  found  in  actual  practice.  The 
corrected  density  will  equal  the  old  density  divided  by  one 
plus  the  change  in  volume.  For  an  illustration  of  such  a 
computation  see  the  set  of  problems  following  this  section. 

Liquids  vary  in  density  more  than  solids,  and  seldom 
is  this  variation  in  direct  proportion  to  the  temperature. 
Water,  for  example,  as  it  is  heated  from  the  freezing-point, 
first  has  a  negative  value  for  its  coefficient  of  expansion 
until  about  4°  C.  is  reached,  when  the  coefficient  changes 
to  a  positive  value.  This  really  means  that  water  contracts 
in  warming  from  0°  C.  to  4°  C.,  and  consequently  has  a 
maximum  density  at  4°  C.  When  the  temperature  varies 
in  either  direction  from  4°  C.,  expansion  takes  place. 

The  density  of  gases  varies  from  an  infinitely  small 
quantity  to  a  value  greater  than  the  same  substance  nor- 
mally has  when  in  the  liquid  state. 

From  Section  44  it  follows  that  the  weight  is  in  pro- 

PV 

portion  to  -=-  and  the  density,  or  weight  per  unit  volume 

will  vary  as  the  weight  divided  by  the  volume,  or 
PV 


then 

W    PV 


Then  for  gases  if  Do  is  the  standard  density  and  Dr  is 
the  density  at  To: 

PoVo 

Do=_Tp_ 
Dr     P2V2' 
T2 


IV 
T2 


96  HEAT 

The  density  of  gas  varies  from  a  value  greater  than  the 
same  substance  has  when  in  the  liquid  state  to  an  infinitely 
small  quantity. 

Problem  34.  What  is  the  density  of  the  products  of  com- 
bustion of  a  furnace  as  they  go  up  an  80-ft.  chimney  at  600°  F.? 
Assume  that  they  weigh  and  act  like  air. 

1  cu.ft.  of  air  under  standard  conditions  weighs  .0817  Ib. 

Let  DT  =the  density  at  600°  F. 

14.7 


.0817      493 


DT        14.7 
1061 


.0817     14.7     1061 
X 


DT       493      14.7 
.0817     1061 


_ 
DT   ~  493  ' 

.0817  X  493 
"1061       ' 

DT  =  .0380. 

Problem  35.  If  the  air  outside  of  the  chimney  in  the  above 
problem  is  at  82°  F.,  what  is  the  density  of  the  air  outside  and 
what  is  the  difference  in  pressure  between  the  outside  and  the 
inside  of  the  base  of  the  chimney? 

P 

.0817      493 


DT          P    ' 
543 

Z)r=.0742. 

The  difference  in  density  is  therefore  .0742  -  .0380  =  .0362  Ib. 
One  foot  height  produces  therefore  a  difference  of  pressure  of 


•IV.     EXPANSION  97 


flQAO 

,0362  Ib.  per  square  foot  or  —rrr  lb.  per  square  inch;  80  ft.  height 
would  produce 

.0362x80' 

—  —  --  =  .0201  lb.  per  square  inch. 
144 

This  corresponds  to  a  draft  of  '—  -  inch  of  water. 

.036 

Problem  36.  If  copper  weighs  .320  lb.  per  cubic  inch  at  24°  C. 
and  has  a  mean  linear  coefficient  of  expansion  of  .0000168,  what 
would  its  density  be  at  364°  C.? 

w  -320 


1  +  . 0000168X340' 
WT  =  .318  lb.  per  cubic  inch. 

Problem  37.  If  the  products  of  combustion  of  a  gas  engine 
have  the  same  density  as  air  and  leave  the  cylinder  at  800°  F., 
find  their  density.  What  was  the  weight  of  the  gases  in  the  cylinder 
if  it  had  an  8-in.  bore  and  a  10-in.  stroke? 

Problem  39.  If  a  120-ft.  chimney  has  a  temperature  inside 
of  300°  C.  and  outside  it  is  20°  C.,  compute  the  difference  of 
pressure  inside  and  outside  in  pounds  per  square  inch  and  the 
draft  in  inches  of  water. 

Problem  40.  If  lead  weighs  .410  lb.  per  cubic  inch  at  60°  F., 
what  would  it  weigh  at  300°  F.? 


HEAT 


REVIEW  PROBLEMS,   CHAPTER  IV 

41.  What  change  takes  place  in  an  iron  tire  whose  diameter 
is  4  ft.  at  a  temperature  of  400°  F.,  when  cooled  to  70°  F.? 

42.  An  iron  bridge  is  300  yds.  long.     Find  play  that  must  be 
allowed  for  a  range  in  temperature  from  —  10°F.  to  120°  F. 

43.  The  end  of  an  iron  boiler  is  a  circle  3  ft.  in  diameter  at 
35°  F.    What  is  the  area  change  when  heated  to  212°  F.? 

44.  A  steel  drum  40  ins.  in  diameter  is  to  have  shrunk  upon 
it  a  steel  collar.    The  shop  temperature  is  60°  F.  and  the  collar 
is  to  be  heated  to  620°  F.    To  what  diameter  should  the  collar 
be  turned  at  shop  temperature  if  it  is  to  have  a  diameter  of  40.050 
when  hot? 

45.  With  what  force  does  a  steel  rail  of  8  sq.in.  cross-section 
tend  to  expand  when  heated  from  40°  F.  to  100°  F.?     (Modulus 
of  elasticity  of  steel  =  30,000,000.) 

46.  A  boiler  tube  has  1.2  sq.in.  cross-section  of  steel.    Cold 
water  at  120°  F.  and  steam  at  200  Ibs.  pressure  pass  alternately 
through  this  pipe.    With  what   force    does  it  tend  to  expand 
lengthwise? 

47.  A  steam  main  of  iron  pipe  having  a  4  sq.in.  cross-section 
is  piped  from  a  boiler  to  an  elbow  which  is  hard  against  a  brick 
wall.    With  what  force  will  the  boiler  be  pushed  away  from  the 
wall  if  piping  was  done  at  22°  C.,  and  steam  is  passed  through 
the  pipe  at  120°  C.? 

48.  A  quantity  of  oxygen  occupies  500  cu.cms.  at  20°  C.,  and 
950  mms.   pressure.    At  what  temperature  would   the  pressure 
be  540  mms.,  if  the  gas  were  allowed  to  expand  to  600  cu.cms.? 

49.  A  quantity  of  air  occupies  10  cu.ft.  at  0°  C.  and  15  Ibs. 
pressure.    What  pressure  will  it  exert  if  the  volume  is  decreased 
to  5  cu.ft.,  and  the  temperature  to  —150°  C.? 

50.  What  would  be  the  effect  of  placing  a  brass  tube  in  a  steel 
boiler  shell  and  making  both  ends  of  the  tube  fast?     Compute 
amount  of  effect  for  a  16-ft,  length  of  tube. 


IV.     EXPANSION  99 


SUMMARY,   CHAPTER    IV 

The  COEFFICIENT  OF  LINEAR  EXPANSION  of  a 
solid  defines  the  rate  of  increase  of  length  due  to  a  rise 
of  temperature.  Numerically  it  is  obtained  by  dividing 
the  increase  in  length  by  the  original  length  and  by  the 
increase  in  temperature. 

For  the  COEFFICIENT  OF  EXPANSION  OF  AN  AREA, 
twice  the  linear  coefficient  may  be  used,  if  the  body 
expands  at  a  uniform  rate  along  all  axes. 

THE  COEFFICIENT  OF  CUBICAL  EXPANSION, 
under  similar  circumstances,  may  be  taken  as  three 
times  the  linear  coefficient. 

Tables  usually  give  only  the  linear  coefficient 
of  expansion  for  solids,  and  the  cubical  coefficient  for 
fluids. 

The  APPARENT  COEFFICIENT  OF  EXPANSION  of 
a  liquid  is  smaller  than  the  true  coefficient  by  the  amount 
of  the  expansion  of  the  containing  vessel. 

The  EXPANSION  OF  A  PERFECT  GAS  obeys  the 
following  laws  providing  that  the  temperatures  are 
high  above  the  critical  point: 

PlVl_P2V2   P3V3* 

Ti   "   T2    "   T3   = 

This  means  that: 

P  varies  as  -  when  the  T  is  constant. 

P  varies  as  absolute  T  (Boyle's  Law)  when  the 
V  is  constant. 


100  HEAT 

V  varies  as  absolute  T  when  the  P  is  constant. 

If  T  varies  as  the  total  heat  energy]  (Charles' 
Law)  in  a  body,  and  if  all  heat  energy  were  taken 
away,  P,  V,  and  T  would  all  be  zero.  From  the  rate 
of  expansion  at  normal  temperatures,  we  find  that 
we  would  reach  such  a  point  at  approximately 
—  273°  C.  and  so  this  point  is  used  as  the  Absolute 
Zero,  or  the  zero  point  of  the  absolute,  centigrade 
scale.  Zero  on  the  absolute  Fahrenheit  scale  is 
-461°  F. 

The  DENSITY  of  any  body  varies  with  its  T,  P,  and 
V,  when  the  body  expands.  Density  should  be  given 
for  a  definite  temperature  only,  and  corrected  when 
applied  to  bodies  at  other  temperatures. 


CHAPTER  V 
THREE  STATES  OF  MATTER 

39.  All  Elements  Have  Three  States.  When  an  element 
is  mentioned  we  usually  form  a  definite  mental  picture 
of  the  substance  with  definite  physical  and  chemical 
properties.  Thus  we  think  of  iron  as  a  hard  gray  solid, 
heavier  than  aluminium  but  not  so  heavy  as  lead,  etc.  Yet 
we  are  all  aware  of  the  change  in  its  ductility  that  takes 
place  at  about  "  red  heat,"  above  which  temperature  it 
is  easily  hammered  into  any  desired  shape.  We  know  that 
it  can  be  melted  in  a  cupola  and  made  a  liquid.  Upon 
reflection  it  is  not  strange  that  all  of  its  properties  should 
be  undergoing  greater  or  less  change  as  its  temperature 
rises.  Age  and  use  may  make  great  changes  in  proper- 
ties such  as  its  magnetism  and  tensile  strength,  even  though 
the  temperature  of  a  substance  remain  unaltered.  Any 
solid  element  may  be  made  a  liquid  or  a  gas  if  heat  intense 
enough  is  supplied  to  reach  the  required  temperature. 
On  the  other  hand  any  gas  may  be  changed  to  a  liquid  or 
to  a  solid  provided  energy  enough  is  taken  from  the  gas 
to  reduce  its  temperature  sufficiently. 

Frequently  solid  compounds  cannot  be  changed  to  liquids 
by  the  application  of  heat  because  of  their  tendency  to 
decompose.  Wood  or  pure  cellulose,  for  example,  when 
heated  never  becomes  liquid,  but  is  broken  up  into  various 
volatile  compounds,  and  solid  carbon  or  charcoal.  It  would 
be  a  very  handy  thing  if  we  could  melt  and  cast  wood. 

Similarly  many  liquids  cannot  well  be  changed  to  gases 
without  their  changing  in  chemical  composition.  Lard,  for 
example,  is  easily  melted  to  a  liquid  and  is  thus  commonly 

101 


102  HEAT 

used.  But  if  liquid  lard  is  heated  too  hot  it  decomposes, 
giving  off  gases  which  do  not  smell  well  and  leaving  behind 
in  the  vessel  a  porous  mass  of  carbon.  Sulphuric  acid  and 
nitric  acid  are  other  illustrations  of  substances  which  change 
in  character  as  they  are  heated  in  air. 

Increasing  the  energy  in  any  substance  or  mixture  of 
substances  always  tends  to  make  chemical  changes  easier. 
When  the  chemist  mixes  liquid  or  solid  substances  in  which 
he  expects  to  produce  some  chemical  action,  if  this  action 
does  not  go  on  as  fast  as  desired,  his  first  thought  is  to  heat 
the  mixture.  This  practice  is  so  common  that  with  the 
chemist  it  is  taken  as  a  matter  of  course. 

There  is  no  single  substance  with  which  we  more 
frequently  come  in  contact  than  water.  In  the  following 
section,  the  changes  that  take  place  in  water  are  more 
fully  discussed  as  an  illustration  of  the  kind  of  changes 
that  take  place  in  all  substances.  The  student  should  not 
think  that  any  of  these  changes  are  peculiar  to  water.  The 
numerical  values  given,  however,  do  not  apply  to  any  other 
substance. 

40.  Ice,  Water  and  Steam.  It  has  already  been  stated 
that  one  B.T.U.  of  heat  energy  delivered  to  1  Ib.  of  pure 
ice  at  0°  F.,  under  standard  conditions  of  pressure,  will  cause 
its  temperature  to  rise  about  2°  F.,  since  the  specific  heat 
of  ice  is  about  .504.  Approximately  16.1  B.T.U.  will  heat 
a  pound  of  ice  from  0°  F.  to  32°  F.  At  this  point  if 
more  heat  energy  is  added  the  temperature  of  the  ice  does 
not  increase,  but  the  ice  begins  to  melt.  The  temperature 
of  the  resulting  mixture  of  ice  and  water  will  remain  at  32°  F. 
until  enough  heat  energy  has  been  delivered  to  it  to  melt 
all  of  the  ice.  This  takes  between  143  and  144  B.T.U. 
After  the  ice  has  all  melted,  then  there  will  be  a  rise  of 
approximately  1°  F.  for  each  B.T.U.  added  until  the  water 
reaches  212°  F.,  when  the  water  begins  to  boil.  The  tem- 
perature of  the  water  will  not  increase  above  212°  F.  after 
boiling  begins  until, it  is  all  boiled  away,  although  in  the 


V.     THREE   STATES  OF  MATTER 


103 


meantime  970  B.T.U.  per  Ib.  must  be  supplied.  For  each 
.50  B.T.U.  supplied  to  this  pound  of  steam,  there  will  be 
thereafter  a  rise  in  temperature  of  approximately  1°  F. 

The  two  succeeding  figures  are  intended  to  graphically 
illustrate  this  change. 

In  Fig.  20,  the  curve  OA  was  plotted  on  the  assumption 
that  the  specific  heat  of  ice  equals  .50  and  is  constant  below 


*Bemp,  Fahrenheit  Absolute 

1  i  I  i  i 

c; 

/ 

n"/ 

/ 

,' 

,• 

x 

/'/ 

?' 

D/i 

y 

/ 

n/ 

/ 

/ 

A/ 

X 

P7 

B' 

/ 

i 

7 

B' 

Temp,  Quantity  Curve 
for  Ice,  Water  and. 
Saturated  Steam 

/ 

/ 

/ 

0    >   JZOO      AGO      600      800      1000     1200     1100     1600 

Total  Heat  in  B,T,U, 
FIG.  20 

freezing.  (Of  course  the  specific  heat  for  the  entire  range 
cannot  be  determined,  as  we  cannot  reach  absolute  zero.) 

AB  shows  the  energy  required  to  change  1  Ib.  of  ice  to 
water. 

BC  shows  the  energy  required  to  raise  the  pound  of 
water  to  the  boiling-point  at  atmospheric  pressure. 

CD  shows  the  energy  to  vaporize  the  water  at  atmospheric 
pressure. 

DD"  represents  the  energy  needed  to  heat  the  pound 
of  steam  to  1100°  F.  absolute,  and  keep  it  saturated  under 
pressure. 


104 


HEAT 


DE  is  the  curve  that  would  result  if  the  steam  had  been 
superheated  at  atmospheric  pressure.  (See  page  133  and 
Table  XL) 

In  general  we  are  not  interested  in  the  energy  contained 
in  ice  below  0°F.,  and  accordingly  Fig.  21  shows  the  total 
energy  per  pound  for  various  temperatures  and  pressures 
above  0°  F. 

A'Ai,  B'C",  DiD",  DiEi,  DE,  and  D'E',  are  not  straight 
lines  because  the  specific  heat  of  the  ice,  water,  and  steam 
is  not  a  constant. 


fiOO 


500 


400 


300 


5200 


100 


r" 

1000  = 

£P« 

ssure 

< 

y,     ^ 

/ 

1 

i 

/ 

Temp.  Quantity  Curve 
for  Ice,  Water,  and 
Saturated  Steam 

ll 

//•E/ 

, 

' 

1 

/ 

j't  

80 

•*P 

•essur 

4 

f 

' 

II 

o/ 

Atm. 

Pre* 

ure 

D 

I 

t 

1 

| 
I 

i 

f 

r 

,/ 

1 

#P 

essun 

D| 

,A, 

/ 

/ 

r~ 

5 

. 

I 

0       200      400       600      800      1000      1200      1100 

Total  Heat  in  B.T.U, 
FIG.  21. 

41.  Latent  Heat.  The  heat  energy  necessary  to  change 
a  unit  mass  of  a  substance  from  the  solid  to  the  liquid  state 
without  change  of  temperature  is  known  as  its  Latent 
Heat  of  Fusion,  or  Latent  Heat  of  Melting. 

It  requires  144  B.T.U.  to  change  ice  to  water  without 
change  of  temperature,  therefore  we  may  call  the  "  latent 


V.  THREE  STATES  OF  MATTER        105 

heat  of  fusion  "  of  ice  or  the  "  latent  heat  of  melting 
of  ice,"  144.  It  is  termed  "  latent  "  (i.e.,  hidden)  because 
these  B.T.U. 's  of  heat  energy  do  not  produce  any  increase 
in  temperature  of  the  ice  or  water  and  so  do  not  have  any 
effect  upon  a  thermometer  in  the  mixture. 

In  the  metric  system,  the  latent  heat  of  fusion,  is  f 
of  144,  or  80. 

Similarly,  the  Latent  Heat  of  Vaporization  is  the 
heat  energy  necessary  to  change  a  liquid  to  the  gaseous 
state  without  change  of  temperature.  To  change  water 
under  standard  conditions  of  pressure  to  steam  at  the  same 
temperature  and  pressure  requires  970  B.T.U.  per  lb.,  or 
970  B.T.U.  Xjj  =539  calories  per  gr. 

To  change  water  from  32°  F.  into  steam  at  212°  F. 
has  taken  180  B.T.U.  +  970  B.T.U.  or  1150.  This  is 
called  the  total  heat  of  steam  at  212°  F.  The  value  of 
the  latent  heat  of  vaporization  is  decreased  by  increasing 
the  pressure.  The  temperature  at  which  boiling  and  freezing 
takes  place  is  also  altered  by  the  pressure. 

Thus  if  we  take  water  at  32°  F.  under  an  absolute 
pressure  of  1  lb.  per  sq.in.  and  add  70  B.T.U.  of  heat 
energy  to  it,  the  temperature  will  reach  102°  F.  It  will 
here  begin  to  boil  and  require  1035  B.T.U.  to  convert  it 
all  to  steam. 

70B.T.U.+  1035  B.T.U.  =  1105  B.T.U.,  the  total  heat 
of  steam  at  102°  F. 

If,  however,  we  take  1  lb.  at  80  Ibs.  per  square  inch 
and  32°  F.,  we  must  add  282  B.T.U.  to  raise  it  312°  F. 
before  it  begins  to  boil,  but  it  takes  only  900  B.T.U.  to 
change  it  all  into  steam. 

282  B.T.U.+  900  B.T.U.  =  1182  B.T.U.,  total  heat  of 
steam  at  312°  F. 

In  Fig.  21  these  facts  are  shown  in  graphical  form.  The 
solid  lines  show  the  result  of  adding  energy  to  the  sub- 
stance at  atmospheric  pressure  14.7  Ibs.  per  sq.in. 


106  HEAT 

CD  is,  accordingly,  the  normal  latent  heat  of  vaporiza- 
tion and  AB  the  latent  heat  of  fusion. 

CiDi  is  the  latent  heat  of  vaporization  at  1  Ib.  pressure. 

C'D'  is  the  latent  heat  of  vaporization  at  80  Ibs.  pressure. 

C"D"  is  the  latent  heat  of  vaporization  at  1000  Ibs. 
pressure. 

It  will  be  noticed  that  these  lines  are  not  equal  in  length, 
showing  that  the  latent  heat  of  water  in  B.T.U.  depends 
upon  the  pressure  under  which  boiling  takes  place.  The 
latent  heat  tends  to  decrease  as  the  pressure  increases. 
Its  amount  at  any  temperature  can  always  be  found  by 
measuring  the  horizontal  distance  between  the  lines  CiC" 
and  DiD"  at  a  height  above  the  X  axis  that  represents 
the  given  temperature. 

The  effect  of  pressure  upon  the  latent  heat  of  fusion 
is  much  less,  and  practically  can  be  neglected,  as  pressure 
only  slightly  affects  the  freezing-point.  It  is  a  peculiar 
fact  that  pressure  lowers  the  freezing-point,  though  we  have 
just  noticed  that  it  raises  the  boiling-point.  The  amount 
of  the  latent  heat  at  temperatures  other  than  32°  F.  can  be 
taken  from  the  curve  just  as  for  vaporization. 

In  Fig.  21  there  are  illustrated  three  different  ways  of 
obtaining  saturated  steam  at  80  Ibs.  pressure,  the  condition 
represented  by  the  point  D'.  If  pure  water  under  1  Ib. 
(absolute)  pressure  is  heated  from  a  temperature  of  32°  F. 
to  the  boiling-point  at  this  pressure,  102°  F.,  70  B.T.U. 
must  be  added.  The  temperature  will  not  rise  further 
(unless  the  water  contains  salts)  until  the  latent  heat, 
1034  B.T.U.,  is  added  to  change  the  water  into  steam. 
The  steam  may  then  have  its  temperature  increased  to 
312°  F.  by  being  mechanically  compressed  and  by  allowing 
78  B.T.U.,  of  the  work  done  upon  it  during  compression 
to  remain  in  the  steam  as  heat  energy.  The  pound  of  steam 
will  then  contain  a  total  energy  above  water  at  zero  degrees 
Fahrenheit  of  1182  B.  T.U. 

If  we  start  with  water  at  32°  F.  and  atmospheric  pres- 


V.  THREE  STATES  OF  MATTER       107 

sure,  we  have  just  seen  that  180+970  or  1150  B.T.U. 
must  be  added  to  change  the  water  to  steam.  To  change 
the  steam  at  atmospheric  pressure  to  saturated  steam  at 
80  Ibs.  pressure  would  require  the  addition  of  32  B.T.U. 
of  mechanical  work.  In  this  process  the  heat  added  in 
each  step  was  different  in  amount  from  that  added  during 
each  corresponding  step  in  the  previous  case  and  yet  the 
total  energy  added  to  form  the  saturated  steam  at  80  Ibs. 
proves  to  be  1182  B.T.U.,  no  matter  what  steps  are  used 
to  bring  the  steam  to  condition  D'. 

If  there  is  salt  in  the  water  the  only  effect  will  be  to 
raise  the  boiling-point  before  evaporation  actually  begins 
and  during  evaporation  as  well.  The  addition  of  a  small 
quantity  of  salt  would  cause  the  line  CiDi  and  C"D",  etc., 
to  be  out  of  parallel  with  the  X  axis.  See  Fig.  21,  in  which 
the  effect  is  shown  for  the  lines  mentioned. 

The  curve  BCC"  is  not  a  straight  line,  but  is  rapidly 
bending  at  C" '.  The  curve  D\DDrf  for  saturated  steam 
goes  up  almost  parallel  with  the  Y  axis  after  crossing  the 
1400  line.  These  two  lines  intersect  a  little  above  675°  F. 
This  is  the  critical  temperature  (see  definition  page  114) 
of  steam  and  theoretically  we  should  have  no  liquid  existing 
above  that  temperature.  If  we  could  actually  see  what 
happens  during  the  process  of  heating  water  at  3000  Ibs. 
pressure  we  would  find  that  the  meniscus  disappears  at 
about  675°  F.,  but  if  we  place  a  suitable  colored  salt  in 
solution  while  we  continue  to  increase  the  temperature  we 
would  probably  find  that  the  volume  below  the  meniscus 
would  still  remain  colored  after  the  critical  temperature  had 
been  passed  and  would  persist  for  several  degrees  above  the 
critical  temperature.  At  the  point  at  which  these  two 
curves  intersect  the  latent  heat  disappears.  Probably  this 
effect  as  well  as  all  of  the  others  which  characterize  the 
critical  temperature  cannot  be  said  to  take  place  at  a  definite 
temperature,  but  between  two  such  temperatures  as  670°  F. 
and  700°  F.  At  this  critical  temperature  the  liquid  loses 


108  HEAT 

the  cohesion  between  its  molecules  which  characterizes 
the  liquid  state.  The  density  of  the  liquid  and  the  gas  is 
the  same  at  the  critical  temperature.  If  the  liquid  is  said 
to  persist  for  a  small  rise  of  temperature  above  the  critical 
temperature  it  is  on  the  assumption  that  the  two  mix  by 
diffusion. 

(Assume  specific  heat  to  be  the  same  as  in  the  tables  unless  given.) 

Problem  1.  How  many  B.T.U.  will  be  required  to  raise  10 
Ibs.  of  lead  to  the  melting-point  and  melt  it  from  a  temperature 
of  60°  F.? 

Heat  to  raise  1  Ib.  to  M.P.     =  (621  -  60)  .0315  =  17.7, 
Heat  to  raise  10  Ibs.  to  M.P.  =  17.7  X  10  =  177, 

L.H.  of  lead =  9.7  B.T.U., 

Heat  to  melt  10  Ibs =  97  B.T.U., 

Total  heat  required =  177+97  =  274  B.T.U. 

Problem  2.  How  many  pounds  of  steam  at  atmospheric 
pressure  will  be  required  to  raise  a  ton  of  boiler-feed  water  to 
200°  F.  from  a  temperature  of  60°  F.,  if  the  steam  is  condensed 
into  the  water? 

1  Ib.  of  steam  has  970  B.T.U.  latent  heat  and  in  cooling  from 
212°  to  200°  gives  up  12  B.T.U.  Total  heat  given  up  per  pound 
therefore  equals 

970+12  =  982  B.T.U.  per  Ib. 

Each  pound  of  cold  water  is  heated,  200-60  =  140°,  and 
therefore  requires  140  B.T.U.  Total  heat  required  =  140x2000 
=  280,000  B.T.U. 

280000     0__  „ 

bteam  required  =          —  =  285  IDS. 
982 

Problem  3.  A  hot  piece  of  steel  weighing  18  Ibs.  is  quenched 
in  15  Ibs.  of  water  originally  at  62°  F.  If  Ij  Ibs.  of  the  water 
boiled  away,  what  was  the  temperature  of  the  steel?  Assume 
the  specific  heat  for  this  range  to  be  .12. 

Heat  gained  =  heat  lost. 

15  Ibs.  of  water  heated  to  212  from  62  require  15  X  (212-  62) 
or  2400  B.T.U. 


V.  THREE  STATES  OF  MATTER       109 

1.5  Ibs.  of  water  changed  to  steam  at  atmospheric  pressure 
require  970  X  1.5  =  1455  B.T.U. 

Total  heat  gained  by  water  =2400 +  1455=  3855  B.T.U. 

If  T  represents  the  initial  temperature  of  the  steam,  and 
.12  is  the  mean  specific  heat,  then  the  heat  lost  by  the  steel 
=  18X.12(r-212). 

3855=  18X.12(T-212). 

qoer 

T=*  ^+212  =  1997°  F. 
zlo 

Problem  4.  How  many  B.T.U.  will  be  required  to  melt  30 
Ibs.  of  zinc  from  a  temperature  of  72°  F.? 

Problem  5.  Ice  is  used  to  cool  a  Prony  brake  which  is  absorbing 
10  H.P.  How  much  ice  is  required  per  hour  if  the  water  escapes 
at  60°  F.  and  the  ice  is  at  28°  F.  when  used? 

Problem.  6.  A  calorimeter  contains  60  gms.  of  water  and  has 
a  water  equivalent  of  80  gms.  Its  temperature  is  20°  C.  200 
gms.  of  ice  and  45  gms.  of  steam  under  standard  pressure  are 
added.  Find  the  resulting  temperature. 

Problem  7.  How  many  pounds  of  water  can  be  evaporated 
from  water  at  212°  F.  to  steam  at  212°  F.  (usually  more  briefly 
written  '"'pounds  of  water  from  and  at  212°  F.")  from  1  Ib.  of  coal 
containing  14,000  B.T.U.,  if  no  heat  is  lost? 

42.  Definitions  and  Distinctions.  The  following  state- 
ments are  familiar,  but  they  will  be  repeated  here  for  ready 
reference. 

The  characteristic  which  we  use  in  defining  a  solid  is 
its  relative  permanence  of  shape  and  volume.  If  pressure 
is  applied  to  a  solid  like  rubber  we  see  it  yield  and  when  the 
pressure  is  released  it  returns  to  its  priginal  shape,  if  the 
pressure  has  not  been  so  great  as  to  strain  the  material 
beyond  its  elastic  limit.  We  therefore  say: 

Solids  have  elasticity  both  of  shape  and  of  volume. 

Liquids  have  no  characteristic  shape,  but  will  take  the 
shape  of  the  containing  vessel.  Their  volume  under  a 
given  pressure  is  absolutely  definite.  With  a  given  liquid, 
if  we  increase  the  pressure  and  temperature,  its  volume  will 
increase  proportionately,  and  if  the  pressure  and  temperature 


110  HEAT 

are  restored  to  their  original  values  the  volume  of  the  liquid 
will  also  return  to  its  original  value.  Therefore  it  is  gen- 
erally true  that: 

Liquids  have  no  elasticity  of  shape,  but  perfect  elasticity 
of  volume. 

Even  the  volume  of  a  given  weight  of  gas  is  uncertain. 
It  depends  upon  both  the  pressure  and  the  temperature. 
Accordingly  we  say: 

Gases  have  elasticity  of  neither  shape  nor  volume. 

Fog  consists  of  small  particles  of  liquid  floating  in  a  gas 
(most  commonly  in  air). 

Vapor  is  a  word  commonly  used  in  speaking  of  a  gas  at 
a  temperature  near  that  at  which  the  liquid  state  of  the 
same  substance  can  exist.  Sometimes  it  is  loosely  used 
to  mean  a  mixture  of  fog  and  gas  of  the  same  substance 
or  even  to  refer  to  fog.  Vapor  is  not  a  good  technical  term. 

Saturation.  A  gas  is .  said  to  be  saturated  (or  a  vapor 
is  said  to  be  saturated)  when  its  weight  per  unit  volume  is 
the  highest  attainable  at  the  given  temperature  and  pressure. 
Saturated  gases  are  usually  found  in  contact  with  their 
liquid  state.  If  heat  energy  is  taken  from  the  gas  and  the 
pressure  kept  constant,  some  of  the  gas  will  be  changed  to 
liquid,  but  the  weight  per  unit  volume  will  remain  the  same. 

The  student  often  asks  if  a  saturated  vapor  is  wet. 
There  are  frequent  cases  where  this  term  is  used  in  the 
following  manner:  The  speaker  knows  that  the  steam 
which  he  is  using  in  his  engine  is  not  superheated  (as  will 
be  seen  later  superheated  steam  contains  no  moisture). 
He  says  it  is  saturated  without  considering  whether  there 
is  any  fog  in  the  steam.  Therefore,  to  be  definite  many 
speak  of  dry  saturated  steam  when  they  wish  to  indicate 
a  quality  of  steam  which  when  passing  through  a  perfect 
steam  separator  would  lose  no  liquid.  However,  the  term 
saturated  steam  should  be  sufficient  to  express  this  idea. 

Saturated  steam  to  the  eye  looks  like  air  or  any  other  gas. 
It  is  colorless  and  transparent.  When  in  winter  steam  blows 


V.  THREE  STATES  OF  MATTER       111 

into  the  air  and  looks  white,  it  is  fog  that  we  see  and  not 
steam.  If  the  student  will  notice  the  exhaust  from  a  loco- 
motive stack  he  will  generally  see  a  zone  immediately  above 
in  which  only  the  smoke  may  be  seen.  Further  up  he  will 
see  a  cloud  of  white.  This  is  the  fog,  or  in  other  words, 
small  drops  of  water  carried  up  by  the  flue  gases. 

A  given  weight  of  gas  at  a  given  temperature,  is  said 
to  be  saturated  when  it  exerts  the  maximum  pressure 
and  has  the  greatest  possible  volume  at  that  tem- 
perature. If  the  student  will  study  Table  IX  he  will 
see  that  this  definition  excludes  both  wet  and  superheated 
steam.  The  values  given  in  Table  IX  apply  only  to 
saturated  steam. 

If  heat  energy  is  taken  away  in  large  enough  quantity 
the  gas  may  all  be  changed  to  liquid,  but  the  temperature 
will  not  change,  unless  the  pressure  changes,  until  all  of 
the  gas  has  been  converted  into  liquid.  Then  if  the  process 
of  taking  away  heat  energy  is  continued,  the  liquid  will  be 
cooled  below  the  temperature  which  it  had  while  in  the  gas- 
eous state. 

If,  on  the  other  hand,  the  temperature  is  kept  constant 
by  immersing  the  vessel  containing  the  gas  and  liquid  in 
a  bath,  any  attempt  to  increase  the  pressure  by  decreasing 
the  volume  will  merely  result  in  more  liquid  being  formed. 
In  that  event  the  weight  of  the  gas  per  unit  volume  will 
remain  constant. 

If  the  mass  of  saturated  gas  just  referred  to  is  led  away 
from  contact  with  liquid  and  while  the  pressure  is  kept 
constant  more  heat  energy  added,  the '  temperature  of  the 
gas  may  be  raised  or  the  volume  may  be  increased  or  perhaps 
both  temperature  and  volume  may  be  increased.  Under 
any  of  these  conditions  the  weight  per  unit  volume  is  less 
than  that  of  saturated  gas  at  the  same  pressure,  and  the  gas 
is  said  to  be  superheated. 

Quality.  When  we  draw  steam  from  a  boiler  it  may 
contain  fog,  or  as  is  sometimes  said,  entrained  water.  A 


112  HEAT 

factor  called  the  quality  of  steam  is  used  to  express"  its 
per  cent  of  dryness.  When  a  number  like  978  is  used  we 
mean  that  97.8  per  cent  of  the  mixture  is  gas.  If  steam  is 
superheated  the  quality  is  denned  by  the  number  of  degrees 
of  superheat.  In  Table  X  this  practice  is  followed. 

The  process  of  changing  a  solid  to  the  liquid  state  is 
called  melting. 

The  reverse  process  is  called  freezing. 

The  process  of  changing  a  liquid  to  the  gaseous  state 
is  called  vaporization.  The  reverse  process  is  called 
condensation. 

Boiling  is  rapid  vaporization,  characterized  by  the 
formation  of  bubbles  in  the  liquid,  which  rapidly  rise  to 
the  top. 

Evaporation  is  frequently  used  to  mean  slow  vaporiza- 
tion without  boiling. 

The  melting-point  of  a  substance  is  the  temperature 
at  a  given  pressure  at  which  the  solid  and  liquid  states 
can  exist  together  as  a  mixture  in  thermal  equilibrium. 

The  freezing-point  is  usually  the  same  as  the  melting- 
point. 

When  a  solid  goes  direct  from  the  solid  to  the  gaseous 
state,  it  is  said  to  sublime. 

When  two  pieces  of  a  solid,  near  its  melting-point, 
like  ice,  for  example,  are  pressed  together  under  large 
pressure  and  then  released  they  are  usually  found  to  have 
frozen  together.  The  process  is  called  regelation. 

The  boiling-point  of  a  substance  in  the  liquid  state  at 
a  given  pressure  is  the  temperature  of  saturated  gas  of 
that  substance  at  that  pressure. 

We  usually  talk  of  the  boiling-point  of  a  liquid  as  being 
a  rather  definite  temperature,  but  a  number  of  common 
experiences  teaches  us  that  it  is  unsafe  to  define  the  boiling- 
point  as  the  temperature  at  which  boiling  takes  place. 
It  is  well  known  that  if  pure  substances  are  used,  they 
may  with  care  be  heated  while  under  atmospheric  pressure 


V.  THREE  STATES  OP  MATTER        113 

far  above  their  normal  boiling-point  without  rapid  evapora- 
tion taking  place.  Then  suddenly  something  may  start  a 
bubble  and  almost  all  the  liquid  may  be  thrown  out  of 
the  vessel  by  the  rapid  boiling  that  will  then  take  place 
and  continue  until  the  liquid  is  cooled  down  to  its  normal 
boiling-point  again. 

The  boiling-point  of  a  liquid  is  always  dependent  upon 
the  pressure  upon  it.  Unless  otherwise  stated,  it  is  always 
assumed  that  a  boiling-point  mentioned  for  a  given  liquid 
is  for  atmospheric  pressure. 

The  presence  of  even  small  quantities  of  solid  impurities 
may  change  the  temperature  of  a  boiling  liquid  from  its 
true  boiling-point;  but  the  gas  developed  will  have  a  tem- 
perature dependent  only  upon  the  pressure  upon  it  during 
formation. 

The  freezing-point  of  a  substance  is  also  greatly  affected 
by  the  presence  of  impurities. 

Frequently  a  determination  of  the  temperature  at  which 
boiling  or  freezing  takes  place  is  resorted  to  in  order  to 
find  out  the  purity  of  the  liquid  in  question.  For  a  further 
discussion  see  Cryogens  in  Chapter  X. 

Air,  indoors  or  out,  always  contains  a  considerable 
amount  of  water  in  the  gaseous  form.  The  ratio,  expressed  in 
per  cent,  obtained  by  dividing  the  weight  per  unit  volume 
of  water  vapor  in  air  at  a  given  temperature  by  the  max- 
imum weight  that  could  exist  in  air  at  that  temperature, 
is  its  relative  humidity. 

The  maximum  pressure  that  water  can  exert  at  any 
temperature  is  called  its  vapor  tension  for  that  temperature. 

The  dew  point  is  the  temperature  to  which  the  atmos- 
phere must  be  cooled  to  have  the  water  contained  in  it 
in  gaseous  form  become  saturated.  During  a  warm  day 
the  air  frequently  takes  up  a  large  amount  of  water  vapor. 
In  that  event  the  vapor  tension  rises,  though  the  rela- 
tive humidity  may  become  either  higher  or  lower  according 
to  the  relative  rate  of  increase  of  the  temperature  and 


114  HEAT 

the  vapor  tension.  As  soon  as  the  air  begins  to  cool,  the 
relative  humidity  rises  until  it  is  100  per  cent,  when  the  dew 
point  is  reached.  The  vapor  being  then  saturated,  con- 
densation takes  place  as  cooling  continues,  and  the  water 
condensed  is  called  dew. 

There  is  a  temperature  for  each  element  and  compound 
above  which  it  cannot  exist  as  a  liquid.  This  temperature 
is  known  as  the  critical  temperature.  Above  the  critical 
temperature  no  amount  of  pressure  will  liquefy  the  substance. 
The  pressure  of  the  dry  saturated  vapor  at  the  critical 
temperature  is  called  the  critical  pressure.  This  is  the 
minimum  pressure  at  which  a  liquid  state  is  possible  at  this 
temperature.  The  numerical  value  of  the  critical  tem- 
perature and  of  the  critical  pressure  defines  the  condition 
of  a  substance  when  it  is  in  the  critical  state. 

To  illustrate:  If  we  want  to  change  air  to  liquid  air 
at  the  highest  possible  temperature  we  must  first  apply  an 
absolute  pressure  of  585  Ibs.  per  square  inch  and  then 
while  maintaining  this  pressure  cool  it  to  a  temperature 
slightly  below  its  critical  temperature,  namely  —220°  F. 
No  amount  of  increase  in  pressure  will  avail  in  produc- 
ing liquid  if  the  cooling  temperature  rises  above  —220°  F. 
If  temperatures  lower  than  —220°  F.  are  used,  a  less  amount 
of  pressure  than  585  Ibs.  per  square  inch  is  required. 

43.  Dalton's  Law.  Suppose  a  chamber  has  a  volume 
of  10  cu.ft.  and  that  it  is  filled  with  a  perfect  gas  (c)  under 
4  Ibs.  pressure.  If  we  compress  this  gas  into  2  cu.ft.  at 
constant  temperature,  we  would  obtain  the  resulting  pressure 
by  Boyle's  law  as  follows: 

VcPc=ViPi     or     10X4  =  2Pi     and     PI  =20.     .     (1) 

Similarly,  if  the  chamber  were  filled  with  a  second 
perfect  gas  (d)  until  its  pressure  were  16  Ibs.  and  the  volume 
reduced  to  8  cu.ft.,  we  would  find : 

V2P2     or     10X16  =  8P2     and     P2  =  20.     .     (2) 


V.  THREE  STATES  OF  MATTER       115 

Now  suppose  this  chamber  to  be  separated  by  a  perfectly 
flexible  diaphragm  into  two  parts  and  on  one  side  is  placed 
the  quantity  of  gas  (c)  which  satisfied  Eq.  (1)  and  on  the 
other  side  is  placed  the  quantity  of  gas  (d)  which  satisfied 
Eq.  (2).  The  resulting  pressure  on  both  sides  of  the 
diaphragm  must  be  equal,  and  by  Boyle's  law  it  follows 
that  the  volumes  are  2  cu.ft.  and  8  cu.ft.  respectively 
and  the  equal  pressures  must  be  20  Ibs.  per  square  inch. 

Now  if  the  diaphragm  were  ruptured  the  gases  would 
diffuse  and  form  a  mixture  of  the  same  general  nature 
as  the  mixture  of  oxygen  and  nitrogen  in  the  air.  The 
gas  (c)  would  then  be  uniformly  distributed  through  the 
whole  10  cu.ft.  and  the  gas  (d)  would  also  be  uniformly 
distributed  through  the  whole  10  cu.ft.  Dalton's  law  says 
that  the  resulting  pressure  will  be  the  pressure  produced 
by  (c)  plus  the  pressure  produced  by  (d)  or  4+16  =  20  Ibs. 
pressure  of  the  mixture.  This  result  is  just  what  we  would 
expect,  as  there  is  no  addition  or  subtrac- 
tion of  heat  energy  when  the  diaphragm 
is  broken  and  consequently  we  would  not 
expect  any  change  of  pressure. 

Dalton's  Law.     When   a  mixture  of 
several  gases  at  the  same  temperature  is 
contained  in  a  vessel,  each  gas  produces 
the  same  pressure  on  the  sides  as  if  the         Mercur 
other  were  not  there,  and  the  total  pres-  Level- 

sure  is  the  sum  of  the  separate  pressures. 

Experimental  Determination   of,  the  FIG.  22. 

Boiling-point.  The  usual  method  of 
finding  the  boiling-point  of  a  liquid  is  to  boil  it  in  a  still 
(see  Fig.  24)  fitted  with  a  thermometer  and  connected  to  its 
condenser.  As  soon  after  the  heat  has  been  applied  as  the 
thermometer  reading  becomes  constant,  the  boiling-point 
may  be  directly  read. 

If  only  a  small  quantity  of  liquid  is  available,  this  method 
is  not  suitable,  and  a  piece  of  apparatus,  shown  in  Fig.  22, 


116  •  HEAT 

is  used.  It  has  already  been  stated  that  the  boiling-point 
of  any  liquid  depends  upon  the  pressure.  The  normal 
boiling-point  of  water  is  100°  C.,  of  course  assuming 
a  normal  atmospheric  pressure  of  760  mm.  or  14.7  Ibs. 
per  square  inch.  The  normal  boiling-point  of  any  liquid 
may  be  defined  as  the  temperature  at  which  the  vapor  of 
the  liquid  exerts  a  pressure  equal  to  normal  atmospheric 
pressure. 

Directions  for  Experiment  H4-2. 

First  a  closed-arm  glass  U-tube,  as  shown  in  Fig.  22,  is  nearly 
filled  with  mercury.  The  remainder  of  the  tube  is  then  filled 
with  the  liquid  to  be  tested  and  the  end  of  the  tube  is  closed. 

By  inverting  and  shaking  the  tube  a  large  part  of  the  liquid  can  be 
made  to  pass  the  mercury  and  collect  in  the  upper  part  of  the  closed 
arm.  The  mercury  is  then  jerked  out  of  the  open  arm  until  it 
stands  considerably  higher  in  the  closed  arm  than  in  the  open  arm. 

Suspend  the  tube  in  a  water  bath  containing  a  thermometer. 
Keeping  the  water  stirred,  gradually  heat  or  cool  the  water  until 
the  mercury  is  exactly  level  in  both  arms.  The  pressure  in  both  arms 
is  then  equal.  The  liquid  will  then  be  seen  to  have  partly  evaporated, 
leaving  a  little  liquid  above,  which  will  be  vapor  at  atmospheric 
pressure.  The  thermometer  in  the  bath  under  these  conditions  will 
read  the  normal  boiling-point. 

Liquids  having  a  normal  boiling-point  above  100°  C.  will  require  a 
bath  of  sulphuric  acid  or  oil. 

If  the  liquid  tends  to  decompose  at  its  normal  boiling-point  its 
boiling-point  at  lower  pressures  is  frequently  obtained.  This  may  be 
done  by  applying  to  the  condenser  a  vacuum  pump  and  manometer 
in  case  the  still  type  of  apparatus  is  used,  or  to  the  end  C.  in  case 
the  U-tube  shown  in  Fig.  22  is  used. 

Determination  of  Freezing-point.  In  Experiment  H7-3,  the 
freezing-point  is  determined  from  a  cooling  curve  plotted  from  the 
readings  of  a  pyrometer  or  thermometer  which  is  frozen  into  the  solid. 
This  method  is  used  because  many  substances  in  passing  from  the 
liquid  state  cannot  well  be  stirred  to  keep  the  whole  mass  at  con- 
stant temperature  and  so  give  a  series  of  readings  that  are  not  very 
easy  to  interpret.  If  the  energy  were  given  out  uniformly  throughout 
the  mass,  the  curve  would  abruptly  stop  in  its  downward  direction 
and  proceed  in  a  horizontal  line  until  the  liquid  had  all  changed  to 
solid,  when  the  curve  would  abruptly  turn  down  again. 


V.  THREE  STATES  OF  MATTER 


117 


The  curve  in  Fig.  23  is  plotted  from  data  taken  in  the  Pratt 
Institute  Laboratories.  Two  pounds  of  lead  were  heated  in  a  small 
crucible  and  after  it  was  thoroughly  melted  the  fire  end  of  a  Bristol 
pyrometer  was  placed  in  the  molten  metal.  The  heat  was  turned  off 
and  readings  of  the  temperature  taken  every  minute  until  after  the 
bend  BC  in  the  cooling  curve  had  been  fully  passed. 

It  is  noticeable  that  there  is  not  a  sharp  turn  at  either  B  or  C. 
This  is  partly  due  to  the  fact  that  the  readings  of  the  pyrometer  lag 
behind  the  true  temperature.  The  fire-end  casing  retards  the  inter- 
change of  heat  energy  between  the  fire  end  and  the  molten  metal. 

44.  Solutions  and  Mixtures.  While  it  is  true  that  there  is 
no  agreement  upon  the  definition  of  SOLUTION  and  MIXTURE,  the 
following  statements  will  help  the  student  to  become  familiar  with 
the  terms. 

A  PHYSICAL  MIXTURE  is  the  result  of  stirring  together  such  sub- 
stances as  chalk  and  sand,  sand  and  water,  oil  and  water,  etc.  The 
substances  may  be  finely 
divided  and  uniformly 
mixed,  but  the  resulting 
mixture  still  consists  of  a 
large  number  of  two  kinds 
of  masses,  each  mass  in 
turn  being  made  up  of  a 
large  number  of  molecules. 
A  solid  substance  mixed  in 
a  liquid  can  often  be 
separated  by  a  process  of 
filtration  by  which  the  solid 
is  strained  from  the  liquid. 
In  cases  where  the  solid 
is  in  a  very  finely  divided 
state,  filtration  may  be  ac- 
complished by  letting  the 
liquid  drain  off  under 
pressure  through  several 
thicknesses  of  finely  woven 
cloth  or  through  filter 
papers. 

SOLUTION  is  a  process  that  results  in  a  more  intimate  association 
of  the  two  substances  involved.  One  of  the  two  substances  is  usually 
a  liquid  and  is  called  the  SOLVENT.  The  second  substance,  which 
is  added  to  this,  is  called  the  SOLUTE.  The  molecules  of  the  solute 
travel  as  individuals  and  uniformly  distribute  themselves  by  a  proc- 


736 

704 

« 
J2672 

I640 
I608 
576 
544 
512 

^A 

\ 

Cooling  Curve 
for  Lead 

\ 

\ 

\ 

[ 

^  O    ( 

•\    o 

c 

X 

)  ^ 

\ 

J 

\ 

, 

5 

468 
Time  in  Minutes 

FIG.  23. 


JO 


118  HEAT 

ess  of  diffusion  through  the  solvent.  The  solution  often  contains 
a  large  number  of  molecules  of  the  solute,  which  have  also  been 
split  up  into  a  positive  and  a  negative  ion.  Thus  the  solution  which 
takes  place  between  common  salt  and  water  or  between  alcohol 
and  water  produces  a  very  different  type  liquid  from  the  emulsion 
or  mixture  resulting  from  a  rapid  shaking  together  of  oil  and  water. 

A  solution  is  said  to  be  saturated  when  the  solvent  will  take  up 
no  more  solute. 

Some  pairs  of  liquids  are  soluble  in  each  other  in  all  proportions, 
alcohol  and  water  for  example.  In  general  when  dealing  with  solu- 
tions of  solids  or  gases  in  liquids  it  is  found  that  there  is  a  definite 
limit  to  the  amount  of  solute  which  a  solvent  at  a  given  temperature 
will  take  up  when  the  solvent  is  in  contact  with  an  excess  of  the  solute. 

The  solubility  of  solids  is  usually  expressed  as  mass  of  solute 
dissolved  per  100  mass  units  of  solvent.  In  the  case  of  gaseous 
solutes  solubility  is  usually  expressed  as  a  ratio  between  the  volume 
of  solvent  and  the  volume  of  solute  dissolved. 

Temperature  has  an  important  effect  upon  solubility.  In  general 
it  is  true  that  in  all  liquid  solvents  solid  solutes  are  more  soluble 
at  high  than  at  low  temperatures  and  all  gaseous  solutes  are  less 
soluble  at  high  temperatures.  Boiling  a  solvent  completely  drives 
off  all  dissolved  gases. 

These  important  facts  are  taken  advantage  of  in  the  chemical 
industry  in  an  infinite  variety  of  ways.  For  example,  with  salt 
solutions  it  is  usual  to  heat  the  solvent  when  it  is  desired  to  increase 
the  amount  of  solute  dissolved.  The  liquor  is  cooled  when  it  is  desired 
to  crystallize  out  some  of  the  dissolved  salt.  Crystalline  solids  are 
often  dissolved  and  recrystallized  to  purify  them.  In  this  event, 
it  is  often  desirable  to  crystallize  by  slowly  evaporating  the  solvent, 
because  the  crystals  are  larger  and  purer. 

Distillation.  When  it  is  desired  to  separate  a  liquid 
solvent  from  a  liquid  solute  or  when  mixtures  of  volatile 
liquors  are  to  be  separated  a  process  called  distillation  is 
resorted  to.  Laboratory  apparatus  for  this  process  is 
shown  in  Fig.  24.  When  a  strong  solution  is  heated  until 
it  boils,  it  will  usually  be  found  that  the  gases  coming 
off  are  mainly  composed  of  the  substances  having  the 
lower  boiling-point.  Thus  in  the  distillation  of  alcohol 
from  water,  proof  spirits  may  be  obtained  from  liquors 
containing  only  a  few  per  cent  of  alcohol. 


V.  THREE  STATES  OF  MATTER 


119 


FRACTIONAL  DISTILLATION  is  resorted  to  when  a  number  of  different 
volatile  substances  having  different  boiling-points  and  different  vapor 
pressures  are  to  be  separated.  In  this  case  the  distillates  obtained 
during  each  successive  rise  of  a  degree  or  so  in  temperature  are  kept 
separate.  The  same  type  of  apparatus  is  used  as  when  it  is  desired 
to  efficiently  separate  two  liquids  at  one  operation.  Various  kinds 
of  still  heads  are  used.  A  still  head  made  of  an  upright  tube  filled 
with  glass  beads  will  give  95  per  cent  alcohol  from  an  18  per  cent 
liquor.  The  hot  gases  rise  to  the  beads  and  partly  condense.  The 
condensed  distillate  drips  backward  to  the  still  in  a  direction  opposite 
to  the  direction  of  flow  of  gases.  These  gases  keep  the  liquid  dis- 
tillate hot  and  in  a  condition  to  give  up  volatile  gases  of  high  vapor 
tension  and  to  absorb  gas  of  low  vapor  tension  and  with  a  high 
boiling-point.  At  the  bottom  of  the  pile  of  beads  the  distillate  will 


FIG.  24. — Apparatus  for  Distillation. 

be  weak  in  the  substance  that  is  being  distilled  because  in  its  down- 
ward path  it  has  taken  up  'excess  of  the  undesirable  gas  and  gives 
off  in  its  place  the  substance  with  the  low  boiling-point  or 
high  vapor  pressure.  This  weak  liquor  constantly  drops  back 
into  the  still.  The  still  is  heated  very  slowly  so  that  the 
distillate  coming  from  the  condenser  will  collect  at  the  most 
efficient  rate.  In  general  the  efficiency  of  the  process  is  increased  by 
lengthening  the  time  of  contact  of  the  liquid  and  gas  in  the  still  head. 
VACUUM  DISTILLATION  is  resorted  to  when  either  the  solute  or 
distillate  tends  to  change  chemically  by  the  heat  necessary  to  drive  off 
the  more  volatile  substance.  In  the  case  of  mixtures  of  organic  sub- 
stances this  method  of  separation  is  very  common.  The  success  of 
the  method  depends  upon  the  fact  that  boiling  takes  place  at  a  much 
lower  temperature  at  reduced  pressures. 


120 


HEAT 


Sugar  is  crystallized  out  of  syrups  in  vacuum  pans,  and  a  great 
many  candies  are  made  in  vacuum  pans  to  avoid  the  chemical  changes 
that  result  if  evaporation  and  cooking  take  place  under  atmospheric 
pressure  at  high  temperatures.  In  commercial  practice  candies  are 
made  at  temperatures  as  low  as  140°  F.  A  reduction  in  boiling- 
point  of  35 °F  is  regularly  obtained. 

Cooling  Towers.  Fig.  25  shows  a  cooling  tower  which  may  be  used 
in  connection  with  a  Refrigerating  Plant  such  as  is  illustrated  in  Fig.  61 


FIG.  25. — View  in  top  of  Water-cooling  Tower,  Showing  Distributor. 

or  with  a  Steam  Power  Plant  such  as  is  shown  in  Figs.  46  and  63. 
The  condensers  in  these  plants  require  a  supply  of  cold  water.  Where 
the  public  water  supply  is  warm  or  expensive  it  is  desirable  to  use  the 
same  water  over  again  as  many  times  as  possible.  To  accomplish 
this  the  water  cooling  tower  is  used.  Hot  water  from  the  condensers 
is  pumped  to  the  top  of  the  tower  and  is  sprayed  over  the  veins  and 
allowed  to  drop  down  to  a  pan  at  the  bottom,  where  it  is  again  col- 
lected. Air  is  allowed  to  blow  through  the  tower  and  as  it  comes  in 


V.     THKEE  STATES   OF  MATTER 


121 


contact  with  the  fine  streams  of  water  a  considerable  amount  of  water 
evaporates.  The  latent  heat  to  support  this  evaporation  is  taken  out 
of  the  main  body  of  the  water  and  thereby  the  water  is  cooled.  The 
cold  water  is  then  returned  to 
the  condenser  by  way  of  a  stor- 
age tank. 

Digesters  are  used  where 
cooking  needs  to  be  done  at  high 
temperatures,  to  extract  oils  or 
to  produce  various  chemical 
changes.  All  of  these  are  closed 
chambers  in  which  cooking  is 
done  at  a  pressure  greater  than 
atmospheric.  On  high  mountains 
these  are  necessary  for  domestic 
cooking  on  account  of  the  lower 
boiling-point  under  the  reduced 
atmospheric  pressure. 

Fig.  26  shows  a  laboratory 
form  of  digester.  Commercial 
forms  of  digesters  are  used  in 
refuse  disposal  plants,  in  fertil- 
izer plants,  in  the  cooking  of 
bones  and  meats,  and  in  the 
extraction  of  oils,  fats,  and 
greases  generally. 

Autoclaves  are  used  for  both 
digesting  and  drying  and  are 
steam-heated  pressure  chambers 
which  can  be  subjected  to 
pressure  or  vacuum.  Cooking 
is  carried  on  in  digesters  by 
turning  on  high- pressure  steam. 
The  pressure  regulates  the  tem- 


perature  and  for  some  operations 
as  much  as  250  Ibs.  are  necessary, 
are  given  by  the  steam  tables. 


FIG.  26.— Digester. 
The  corresponding  teniperatures 


In  Fig.  27  a  type  of  pressure  cooker  is  shown  which  is 
now  commonly  used  in  mountainous  regions  for  cooking 
vegetables  and  foods  that  are  ordinarily  boiled.  It  is 
claimed  that  foods  cook  very  much  more  quickly  at  a 


122 


HEAT 


pressure  of  about  35  Ibs.  absolute  and  require  less  fuel. 
The  reason  for  this  will  be  understood  if  the  student  will 
notice  in  the  steam  table  the  temperature  at  which  water 
boils  at  35  Ibs.  pressure.  The  slight  increase  in  tem- 
perature above  212°  F.,  greatly  increases  the  speed  at 
which  the  starch  grains  are  broken  up  and  consequently 

the  time  required^  for  cooking 
is  reduced. 

45.  Analysis  of  Latent  Heat 
of  Vaporization.  Fig.  28  repre- 
sents a  cylinder  of  indefinite 
length  and  of  1  sq.ft.  (144 
sq.in.)  area  of  base,  fitted  with 
a  frictionless  piston.  Suppose 
there  is  in  it  1  Ib.  of  water  at 
32°  F.  This  amount  of  water 
would  occupy  ^4^  =  .0160  cu. 
ft.,  and  since  the  area  of  the 
base  is  1  sq.ft.  the  water  would 
stand  .0160  ft.  high  in  the 
cylinder.  As  the  upper  end  of 
the  cylinder  is  open,  there 

would  be  14.7  Ibs.  per  square  inch  on  the  piston  or  a  total 
of  2117  Ibs.,  which  would  have  to  be  overcome  in  pushing 
the  piston  up. 

First  Step.  Now  suppose  heat  were  applied  to  water. 
The  temperature  would  rise  to  212°  F.  after  180.5  B.T.U. 
were  applied,  and  the  piston  would  remain  about  stationary. 
Second  Step.  As  more  heat  is  added,  the  water  is  grad- 
ually changed  to  steam  and  the  piston  gradually  rises  to 
make  room  for  the  steam,  as  1  Ib.  of  steam  at  atmospheric 
pressure  requires  26.8  cu.ft.  Thus  when  all  water  has  been 
converted  into  steam,  the  piston  has  risen  26.8  ft.  as  in 
Fig.  29.  In  doing  this  it  has  acted  against  a  pressure  of 
2117  Ibs.  and  has,  therefore,  done  2117X26.8  =  56,700 


FIG.  27. — Pressure  Cooker 
for  Family  Use. 


V.     THREE  STATES  OF  MATTER  123 

ft.-lbs.  of  work.     Since  1  B.T.U.  does  780  ft.-lbs.  of  work, 


to  do  those  56700  ft.-lbs.  must  have  required 


=  72.8 


B.T.U.  Now  we  know  that  970  B.T.U.  are  given  to  1  Ib. 
of  water  when  it  is  changed  to  steam  at  atmospheric  pressure. 
Since  only  72.8  B.T.U  of  this  heat  are  used  up  in  doing  the 
external  work  or  raising  the  piston,  the  rest,  970  —  72.8  or 
897  B.T.U.  ,  must  be  used  in  doing  the  internal  work  of 
overcoming  the  molecular  forces. 


3 

[!• 

^01 

T 

I 

"i" 

^    Steam 

il 

t 

FIG.  28. 


FIG.  29. 


The  total  amount  of  heat  given  to  the  water  to  change 
it  to  steam  may  then  be  summarized  as  follows: . 

(1)  Raising  temperature  of  water  from  32°  to  212°     180 

(2)  Overcoming  internal  resistance 897 

(3)  Overcoming  external  resistance 73 


Total  heat.  .  ,1150 


124  HEAT 

From  the  foregoing  it  will  be  seen  that  latent  heat  of 
vaporization  may  be  said  to  be  made  up  of  two  parts:  namely, 
first,  the  energy  necessary  to  separate  the  molecules  or  to 
overcome  the  internal  resistance  to  expansion,  and,  second, 
the  energy  to  overcome  the  external  resistance  to  expansion. 

In  the  steam  tables  will  be  found  a  column  showing  the 
external  work  at  various  pressures,  and  in  Figs.  32  and  33, 
pages  128  and  129,  will  be  found  curves  showing  both  the 
internal  and  the  external  work.  The  internal  work  may  be 
found  by  subtracting  the  external  work  from  the  latent  heat. 

46.  Relation  between  the  Pressure  and  Temperature  of 
Steam.  The  vapor  tension  of  water  at  various  temperatures 
is  a  quantity  constantly  entering  into  the  computations 
of  the  chemist  and  the  engineer.  It  is  given  by  various 
tables  and  always  forms  the  basis  of  "  steam  tables."  So 
common  are  steam  tables  that  saturated  steam  is  often 
defined  as  steam  at  the  temperature  and  pressure  given 
in  the  tables.  Saturated  steam  may  be  expected  when- 
ever the  liquid  state,  water,  and  the  gaseous  state,  steam, 
exist  together.  If  the  steam  is  saturated  any  attempt  to 
decrease  the  volume  without  a  change  of  temperature 
will  result  in  condensation  of  part  of  the  steam.  On  the 
other  hand,  an  increase  in  the  volume  allotted  to  the  steam 
will  cause  it  to  expand  and  its  temperature  to  fall  below 
that  of  the  liquid.  The  pressure  will  also  tend  to  decrease 
and  the  liquid  will  undergo  a  lowering  of  boiling-point. 
The  liquid  will  then  boil  violently  until  a  condition  of 
equilibrium  is  reached. 

When  a  steam  boiler  explodes,  the  water  in  it  is  at  a 
high  pressure  before  the  explosion  and  consequently  above 
its  normal  boiling-point.  As  soon  as  the  boiler  lets  go,  the 
boiling-point  changes  and  the  large  amount  of  energy  goes 
into  evaporating  much  of  the  water  into  steam.  This 
accounts  for  the  remarkably  large  amount  of  steam  that 
escapes  and  endangers  any  who  are  near. 

Since  saturated  steam  is  steam  in  equilibrium  with  its 


V.  THREE  STATES  OF  MATTER 


125 


liquid  phase,  water,  at  the  given  pressure,  the  temperature 
of  the  saturated  steam  is  the  same  as  the  boiling-point  of  the 
liquid  at  that  pressure.  Therefore  a  knowledge  of  the 
pressure  in  any  steam  boiler  also  gives  us  a  knowledge 
of  the  temperature  of  both  the  water  and  the  steam  in  it 
by  simply  referring  to  our  steam  tables  or  to  the  pressure 
temperature  curves  such  as  are  given  in  Plate  1. 

47.  Experimental  Determination  of    Relation  between 
the  Pressure  and  Temperature  of  Steam.     In  Experiment 


FIG.  30. — Simplified  Section  of  Fig.  31. 

31-3  the  student  determines  this  relation  and  plots  a  curve 
of  his  results  obtained  with  the  laboratory  apparatus. 
This  curve  is  then  compared  with  one  plotted  on  the  same 
sheet  from  the  data  given  in  the  steam  tables  in  the 
Appendix. 


126 


HEAT 


The  apparatus  used  is  shown  in  Figs.  30-31,  and  is 
a  simple  form  of  that  used  by  Henri  Victor  Regnault 
(1810-1878).  He  made  a  series  of  experiments  which  are 


FIG.  31. — Small  Boiler  for  Obtaining  the  Steam  Table  Constants. 

classical  on  the  properties  of  water  and  steam  and  other 
liquids   and   gases.     His  work  has  been  checked   and   his 


V.  THREE  STATES  OF  MATTER       127 

results  corrected,  but  they  were  remarkably  accurate  con- 
sidering the  facilities  with  which  he  worked. 

DIRECTIONS 

In  abbreviated  form  the  directions  for  Experiment  No.  Hl-3 
follow. 

It  is  desired  in  this  experiment  to  determine  the  temperature  of 
steam  for  pressures  ranging  from  about  3  Ibs.  per  square  inch  to  about 
40  Ibs.  per  square  inch. 

The  apparatus  is  to  be  arranged  as  in  the  diagram.  Pressures  are 
controlled  by  exhausting  air  from,  or  forcing  air  into  the  large  air 
chamber  A.  Steam  is  generated  in  the  boiler  B,  which  communicates 
with  A.  A  portion  of  the  connecting  tube  is  surrounded  by  a  jacket 
G,  through  which  cold  water  is  passed  to  condense  the  steam  as  formed. 
Pressure  in  the  closed  system  is  to  be  measured  by  a  manometer  at 
M  or  by  a  pressure  gauge,  and  the  corresponding  temperature  of  the 
steam  in  the  boiler  is  to  be  read  from  the  thermometer,  T. 

The  thermometer  should  be  pushed  well  down,  so  that  the  bulb 
extends  into  the  body  of  the  boiler.  It  must  not,  however,  extend  into 
the  water.  All  connections  must  be  air  tight. 

In  securing  readings,  first  connect  tube  E  with  aspirator  and  reduce 
the  pressure  in  A  until  a  difference  in  level  of  about  600  mm.  is  shown 
by  the  manometer.  Then  close  the  pinch  cock  at  Vi,  and  disconnect 
from  the  aspirator.  Place  the  Bunsen  burner  under  the  boiler  and 
see  that  water  is  passing  through  the  condenser.  The  burner  should 
at  all  times  be  turned  down  so  that  the  flame  will  not  flare  up  about 
the  boiler.  A  small  flame  will  be  sufficient  at  first,  as  the  boiling 
point  will  not  be  high.  Continue  to  boil  the  water  at  this  temperature 
until  the  thermometer  ceases  to  rise — five  or  ten  minutes  will  probably 
be  required.  Then  record  thermometer  reading  and  the  difference 
in  level  of  manometer  columns.  Record  also  height  of  barometer. 
Next  open  the  valve  at  V\t  holding  the  finger  over  the  open  ends 
of  the  tube  meanwhile,  and  carefully  admit  air  until  the  difference 
in  level  of  manometer  columns  is  diminished  to  about  500  mm.  Boil 
the  water  at  this  pressure  until  the  thermometer  shows  constant 
temperature  and  record  manometer  and  thermometer  readings  as 
before.  Proceed  in  this  way  by  about  equal  steps,  increasing  the 
pressure  75  to  100  mm.  at  a  time  until  atmospheric  pressure  is  reached, 
i.e.,  pinch  cock  E  is  left  open  while  the  reading  is  taken. 

Then  connect  the  aspirator  tube  E  to  a  compression  pump  and 
force  air  into  A  until  the  maximum  pressure  required  in  the  experi- 
ment is  reached.  Do  not  force  the  mercury  by  the  bend  in  the  manometer. 


128 


HEAT 


1040     82    200      940 


1000    78 


Sfl) 


800     58          0     700         0     1070 


GO  80  100 

1    PRESSURE 


FIG.  32. 


V.     THREE   STATES   OF  MATTER 


129 


PROPERTIES 

OF 

SATURATED 
STEAM 


140        .160         180         200         220         240         260        280         300        320        340 
1   PRESSURE 


FIG.  33. 


130  HEAT 

Decrease  the  pressure  by  successive  steps  of  about  100  mm. 
as  before  and  take  readings  until  at  least  ten  readings  of  temperature 
and  pressure  have  been  secured  between  the  lowest  and  the  highest 
temperatures. 

The  main  precautions  to  be  taken  are,  to  keep  the  condenser  always 
cold,  to  allow  plenty  of  time  for  the  thermometer  to  come  to  steam 
temperature,  and  to  keep  the  flame  away  from  the  thermometer  tube. 

48.  Steam  Tables.  Steam  tables  have  already  been 
referred  to  as  giving  the  relation  between  the  pressure  of 
saturated  steam  and  its  temperature.  We  may  illustrate 
the  use  of  Table  IX  by  looking  up  the  properties  of  saturated 
steam  at  235  Ibs.  gauge-pressure.  In  Column  1  we  find 
absolute  pressure  given.  Using  only  the  three  significant 
figures,  250  Ibs.  absolute  will  be  the  correct  pressure  to 
look  up.  In  Column  2  on  the  same  line,  we  find  the  tem- 
perature of  saturated  steam  at  250  Ibs.  absolute  to  be  401°  F. 
The  temperature  given  on  any  line  is  also  the  boiling-point 
at  the  pressure  recorded  at  the  beginning  of  the  line.  Thus 
the  boiling-point  at  250  Ibs.  absolute  is  401°  F.  Column  3 
gives  the  total  heat  energy  in  B.T.U.,  which  must  be  supplied 
to  1  Ib.  of  water  at  32°  F.  to  raise  it  to  dry  saturated  steam 
at  a  pressure  given  on  the  same  line  in  Column  1.  At 
250  Ibs.  the  total  heat  energy  is  1201  B.T.U.  Column  4 
gives  the  volume  that  1  Ib.  of  dry  saturated  steam  would 
occupy  at  the  pressure  given  in  Column  1.  At  250  Ibs. 
dry  saturated  steam  has  a  specific  volume  of  1.845  cu.ft. 
The  reciprocal  of  the  value  in  Column  4  gives  the  value 
in  Column  5.  One  cubic  foot  of  dry  saturated  steam 
at  250  Ibs.  weighs  .542  Ib.  Column  6  gives  the  B.T.U. 
required  to  heat  the  liquid  to  the  boiling-point.  At  250 
Ibs.,  374.2  B.T.U.  are  required.  Column  7  gives  the  latent 
heat;  at  250  Ibs.  the  energy  to  evaporate  1  Ib.  of  water 
is  826.9  B.T.U.  Columns  8  and  9  show  this  latent  heat 
to  be  analyzed  into  741.5  B.T.U.  heat  energy  to  overcome 
internal  molecular  forces  and  85.4  B.T.U.  of  external  work. 

Caution.     The  student  will  always  remember  that  the 


V.  THREE  STATES  OF  MATTER        131 

pressures  in  the  table  are  absolute,  while  the  customary 
way  of  stating  boiler  pressures  is  to  give  the  gauge  pressure, 
which  is  always  pressure  above  atmospheric.  Therefore 
to  gauge  pressure  as  given  should  be  added  14.7  Ibs.  before 
referring  to  the  table. 

Problem  8.  How  many  B.T.U.  are  required  to  raise  1  Ib. 
of  water  from  72°  F.  to  steam  at  80  Ibs.  absolute  pressure? 

The  temperature  corresponding  to  80  Ibs.  pressure  in  the  steam 
table  is  312°  F. 

Heat  of  liquid  above  32°  F.  =  282.2  B.T.U. 
Heat  of  liquid  above  72°  F.  =  282.2-40=  242.2  B.T.U. 
Latent  heat  =  899.8. 

Total  heat  above  72°  F.  therefore  =  242.2  +  899.8  =  1142 
B.T.U.,  heat  required. 

Problem  9.  How  many  pounds  of  water  from  and  at  212° 
F.  would  this  energy  in  Problem  1  evaporate? 

1   Ib.   of  water  from  and  at    212°  F.  requires  970  B.T.U., 

1142 
therefore  — — -  =1.18  Ibs.  will  be  evaporated  by  1142  B.T.U. 

t7  /  U 

Problem  10.  How  many  foot-pounds  of  energy  are  required  to 
evaporate  a  ton  of  water  from  a  temperature  of  60°  F.  to  steam 
at  120  Ibs.  (gauge)  pressure? 

The  steam  table  gives  the  total  heat  of  steam  above  32°  F. 
at  120+14.7,  or  134.7  as  1191  B.T.U.  Total  heat  above  60° 
F.  would  be  28  B.T.U.  less,  or  1163  B.T.U.  As  there  are  778 
ft.-lbs.  per  B.T.U.  and  2000  Ibs.  per  ton,  the  total  work  in  foot 
pounds  per  ton  =778x2000x1 163  B.T.U.  =1.81  XlO9  B.T.U. 

Problem  11.  How  many  pounds  of  water  would  this  energy 
evaporate  from  and  at  212°  F.? 

Since  it  takes  970  B.T.U.  to  evaporate  1  Ib.  of  water  from 
and  at  212°  F.,  the  equivalent  evaporation  will  be 

2000  *1163  =  2400  Ibs.  of  water. 
970 


Problem  12.    If  coal  as  fired  contains  5  per  cent  moisture  and 

13,300  B.T.U.  of  energy,  how  much  of  the  energy  is  required 

/to  evaporate  this  5  per  cent  of  water  and  heat  it  to  the  tern- 


132  HEAT 

perature  of  the  escaping  flue  gases,  600°  F.?  Assume  as  an  average 
specific  heat  of  steam  =  .70.  Assume  the  temperature  of  the 
coal  as  fired  to  be  72°  F. 

In  every  pound  of  coal  .05  Ib.  of  water  has  to  be  heated  from 
72°  F.  to  212°  F.,  evaporated  and  then  the  steam  heated  to  600° 
F.  This  requires  .05(140.3  +970  +388  X.  70)  =65.1  B.T.U. 

Problem  13.  If  the  dried  sample  of  the  coal  fired  under  the 
above  conditions  had  tested  out  14,000  B.T.U.  what  would  have 
been  the  available  energy  from  the  coal  if  each  pound  as  fired 
contained  5  per  cent  moisture? 

Since  only  95  per  cent  was  really  coal,  there  was  only 
14000  X  .95  or  13300  B.T.U.  of  energy  in  the  coal.  The  water 
wasted  65  B.T.U.  and  there  were  therefore  only  13,235  B.T.U. 
of  available  energy  left. 

Problem  14.  How  many  pounds  of  water  must  circulate  through 
a  condenser  such  as  shown  in  Fig.  24  to  distill  5  gals,  of  absolute 
alcohol  if  the  circulating  water  enters  the  condenser  at  40°  F. 
and  leaves  it  at  160°  F.  and  if  the  alcohol  leaves  the  condenser 
at  a  temperature  of  60°  F.?  (Compute  according  to  British 
system.) 

Five  gallons  of  alcohol  having  a  specific  gravity  of  .794  weigh 
10  X  .794  X  5  =  39.7  Ibs.  (English  gal.  of  water  =  10  Ibs.) 

If  the  latent  heat  of  absolute  alcohol  is  369  B.T.U.,  the  boiling- 
point  159°  F.,  and  the  specific  heat  of  the  liquid  is  .50,  then  the 
energy  lost  by  the  alcohol  will  equal 

39.7(369  +  .50x99)  =16600  B.T.U. 

Let  x  equal  the  weight  of  circulating  water  required. 
Then  the  heat  gained  by  the  water  will  equal 


(160-40)z  = 
Since  heat  gained  =  heat  lost, 

120^  =  16600, 
x  =  138  Ibs. 

Problem  15.  A  steam-heated  vacuum  pan  takes  out  50  Ibs. 
of  water  per  hour  from  a  sugar  solution.  If  the  pan  receives 
steam  at  100  Ibs.  pressure  and  wastes  5  Ibs.  of  steam  per  hour 
in  keeping  it  hot,  what  is  the  total  weight  of  steam  used  per  hour? 

Assume  a  vacuum  in  the  pan  of  28  ins.  of  mercury  or  an  absolute 


V.  THREE  STATES  OF  MATTER       133 

pressure  of  1  lb.,  neglect  any  heat  required  to  heat  the  solution 
to  the  boiling-point,  and  assume  that  steam  is  returned  to  the 
boiler  at  102°  F. 

Total  heat  to  evaporate  50  Ibs.  water  from  and  at  101.8° 
F.  =1035  X50  =51750  B.T.U. 

If  x  =  weight  of  steam  required  to  yield  51750  B.T.U.,  the 
heat  given  up  will  also  equal  the  difference  between  the  total  heat 
of  steam  at  100  Ibs.  gauge  and  the  heat  of  the  condensed  liquid 
at  102°F.  =  1189-70  =  1119.r. 

Heat  lost  =  heat  gained, 
1119z  =  51750, 

x  =  46.2  Ibs., 
Total  steam  =  51.2  Ibs. 

Problem  16.  What  temperature  can  be  obtained  in  a  steam 
cooker  or  digester  using  steam  at  160  Ibs.  gauge  pressure? 

Problem  17.  How  much  energy  will  be  left  in  the  cooker  per 
pound  of  steam  used  if  the  cooker  maintains  this  temperature? 

Problem  18.  Suppose  a  steam  drier  is  used  with  a  temperature 
as  high  as  can  be  obtained  with  60  Ibs.  steam  pressure.  If  this 
completely  dries  200  Ibs.  of  coal  per  hour,  containing  8  per  cent 
moisture,  how  much  steam  will  the  drier  use  if  the  coal  is  taken  in 
at  60°  F.? 

Assume  the  coal  to  have  a  specific  heat  of  .32  and  to  be  ejected 
from  the  drier  at  the  temperature  of  the  steam. 

Problem  19.  How  many  pounds  of  circulating  water  will 
be  required  to  condense  10  gals,  of  ethyl  alcohol  to  a  temperature 
of  100°  F.,  if  the  tap  water  temperature  is  60°  F.  and  the  over- 
flow from  the  condenser  is  at  90°  F.? 

Problem  20.  A  boiler  evaporates  800  Ibs.  of  water  an  hour 
from  a  temperature  of  60°  F.  at  a  pressure*  of  60  Ibs.  gauge.  Find 
equivalent  evaporation  from  and  at  212°  F. 

49.  Superheating  Steam.  If  dry  steam  is  not  saturated 
it  will  be  superheated.  Referring  to  the  statements  made 
above  it  will  be  seen  that  if  the  temperature  of  steam  is 
reduced  and  the  pressure  kept  constant,  it  still  remains 
saturated,  but  some  of  it  will  be  condensed.  If  th»  tem- 
perature of  the  gas  is  increased,  and  the  pressure  kept  constant 


134  HEAT 

or  below  that  of  saturated  vapor  at  the  new  temperature, 
the  gas  is  said  to  be  superheated  or  unsaturated. 

Superheated  steam  is  steam  at  a  temperature  too  high 
to  agree  with  that  given  in  the  steam  table  for  the  pressure 
at  which  the  steam  is  confined.  Or  superheated  steam  is 
steam  at  a  temperature  above  the  boiling-point  of  water 
for  the  pressure  at  which  the  steam  exists. 

The  total  heat  of  steam  is  increased  about  .65  B.T.U. 
for  each  degree  Fahrenheit  of  superheating  up  to  100°  F., 
and  averages  about  .75  B.T.U.  for  200°  F.  of  superheating. 
This  variation  is  due  to  the  fact  that  the  specific  heat  of 
steam  increases  with  the  temperature. 

See  Table  XI. 


V.     THREE  STATES  OF  MATTER  135 


REVIEW   PROBLEMS,    CHAPTER  V. 

21.  How  many  B.T.U.  are  required  to  raise  the  temperature 
of  195  Ibs.  of  water  from  32°  F.  to  212°  F.  and  evaporate  it? 

22.  How  many  pounds  of  water  can  be  evaporated  from  and 
at  212°  F.,  in  a  boiler  having  an  efficiency  of  75  per  cent,  using 
coal  containing  13,200  B.T.U.? 

23.  If  dry  coal  contains  14,200  B.T.U.  how  much  does  5  per  cent 
of  moisture  reduce  the  fuel  value  per  pound  of  coal  purchased? 
Consider  only  the  latent  heat  of  the  moisture  in  this  problem. 

24.  If  coal  contains  2  per  cent  moisture,  how  much  does  it  affect 
the  heat  available  from  the  coal  if  the  fuel  is  stoked  at  80°  F., 
and  flue  gases  have  a  temperature  of  560°  F.?    Express  the  result 
in  B.T.U.  lost  per  pound. 

25.  Coal  is  burned  under  a  boiler  and  the  products  of  combustion 
go  up  the  flue  at  a  temperature  of    600°  F.     The  boiler-room 
temperature  is  60°.    The    coal    contains  10  per  cent    moisture. 
A  sample  after  drying  gives  14,400  B.T.U.  per  Ib.  of  dry  sample. 
If  20  Ibs.  of  air  per  pound  of  wet  coal  used  are  required  for 
smokeless  combustion,  how  many  B.T.U.  go  to  heat  water  in 
the  boiler?     (Assume  no  heat  lost  due  to  radiation,  leaks  in  boiler 
setting,  etc.) 

26.  The  energy  from  1  Ib.  of  coal  yielding  14,000  B.T.U.  will 
melt  how  many  pounds  of  ice? 

27.  A  25-lb.  cake  of  ice  requires  how  much  coal  to  melt  it  and 
warm  the  resulting  water  to  78°  F.?    Coal  gives  14,250  B.T.U. 
per  pound. 

28.  From  the  B.T.U.  per  pound  latent  heat  of  vaporization  of 
mercury  as  given  in  the  table,  find  the  calories  per  gm. 

29.  Find  latent  heat  of  alcohol  in  B.T.U.  per  pound. 

30.  20  Ibs.  of  lead  in  a  crucible  were  allowed  to  cool  from  a 
high  temperature  and  a  curve  plotted.     From  this  it  was  deter- 
mined that  the  rate  of  change  of  cooling  just  before  solidification 
took  place  was  41°  F.  per  minute  and  directly  after  39°  F.  per 
minute.     The   temperature  remained   constant  for  7.5    min.     If 
cooling  was  going  on  at  the  mean  rate  obtained  by  averaging  these 
given  above,  what  must  be  the  latent  heat  of  the  lead? 


136  HEAT 

31.  What   is  the  efficiency  of   a  boiler  which  vaporizes  8  Ibs. 
of  water  at  75°  F.  to  steam  at  90  Ibs.  pressure  for  every  pound 
of  coal  burned?     The  coal  has  13,800  B.T.U.  per  Ib. 

32.  How  many  foot-pounds  of  energy  are  necessary  to  change 
1  Ib.  of  ice  at  32°  F.  to  water  at  32°  F.? 

33.  How  many  foot-pounds  of  energy  are  necessary  to  change 
1  Ib.  of  water  to  steam  from  and  at  normal  atmospheric  pressure? 

34.  How  many  foot-pounds  of  energy  are  necessary  to  change 
1  Ib.  of  ice  at  32°  F.  to  steam  at  atmospheric  pressure? 

35.  If  for  each  pound  of  coal  burned  in  the  boiler  furnace 
10  Ibs.  of  water  at  70°  F.  are  converted  into  steam  at  350°  F., 
what  is  the  ratio  of  the  heat  given  to  the  steam  to  the  heat 
value  of  1  Ib.  of  coal,  the  latter  being  14,500  B.T.U.? 

36.  How  many  pounds  of  ice  at  32°  can   be  melted  by  3  Ibs. 
of  steam  at  30  Ibs.  pressure  (absolute)? 

37.  If  4  Ibs.  of  steam  at  14.7  Ibs.  pressure  be  led  into  100 
Ibs.  of  water  at  42°  F.,  and  the  resulting  temperature  is  85.6° 
F.,  what  is  the  latent  heat  of  steam  at  this  pressure? 

38.  A  steam  boiler  evaporates   19  Ibs.  of  water  from  and  at 
212°  F.  per  pound  of  coal  used,  and  the  coal  costs  $3.50  per  ton. 
Find  the  cost  of  producing  1  ton  of  steam  at  80  Ibs.  pressure  from 
water  at  72°  F.,  assuming  a  constant  efficiency. 

39.  In  1884  the  A.S.M.E.  defined   one  JB.H.P.  as   cither  (1) 
30  Ibs.  of  water  evaporated  from  a  feed-water  temp,  of  100°  F. 
to  steam  at  70  Ibs.  pressure,  or  (2)  34.5  Ibs.  of  water  evaporated 
from  and  at  212°  F.     From  your  tables  reduce  the  second  value 
to  weight  of  water  evaporated  under  the  first  conditions. 


V.  THREE  STATES  OF  MATTER        137 


SUMMARY,   CHAPTER  V 

Certain  substances  like  water  are  constantly  changing 
their  states  during  familiar  processes.  We  describe  their 
condition  by  such  words  as  solid,  liquid,  gas,  fog, 
vapor,  saturated  vapor,  superheated  gas,  dew,  relative 
humidity,  vapor  tension.  The  process  of  changing 
state  we  describe  as  freezing,  melting,  sublimation, 
regelation,  boiling,  condensation,  vaporization,  etc. 
All  substances  may  have  these  terms  applied  to  them 
and  may  pass  through  all  of  the  states  mentioned. 
We  study  water  because  it  is  the  compound  most 
frequently  used. 

LATENT  HEAT  OF  MELTING  is  the  energy  required 
to  change  the  state  of  a  substance  from  solid  to  liquid 
without  changing  the  temperature. 

LATENT  HEAT  OF  VAPORIZATION  is  the  energy 
required  to  change  the  state  from  liquid  to  gas  without 
change  of  temperature. 

The  amount  of  the  latent  heat  depends  upon  the 
pressure  during  the  change  of  state. 

DALTON'S  LAW  states  that  the  pressure  produced 
by  a  mixture  of  gases  in  an  inclosed  space  is  equal 
to  the  sum  of  the  individual  pressures  that  each  gas  would 
have  if  the  other  gases  were  taken  out  of  the  space  in 
question. 

All  elements  may  be  made  to  change  state  after  the 
manner  of  water,  but  some  solid  compounds  cannot  be 
changed  to  liquids  because  decomposition  results  upon 


138  HEAT 

the  application  of  heat.  Other  compounds  may  be 
changed  to  the  liquid  state,  but  they  decompose  before 
becoming  gases. 

PHYSICAL  MIXTURES  are  mass  mixtures. 

Solutions  are  mixtures  of  different  kinds  of  mole- 
cules in  which  the  molecules  of  the  two  or  more  kinds 
travel  about  as  independent  units  through  the  mass. 

The  solute  is  said  to  uniformly  distribute  its  mole- 
cules through  the  solvent  by  a  process  of  diffusion. 

DISTILLATION  is  accomplished  by  taking  advantage 
of  the  different  boiling-points  of  the  various  substances 
in  a  mixture  or  solution  to  effect  a  separation. 

Latent  heat  of  Vaporization  may  be  analyzed  into 
(i)  External  work,  work  done  against  the  atmosphere 
in  expanding  from  the  original  volume  of  the  water, 
and  (2)  Internal  work,  or  the  work  necessary  to  over- 
come the  molecular  forces. 

The  PRESSURE-TEMPERATURE  ratio  is  not  constant 
for  steam  at  a  fixed  volume;  and  there  is  no  exact 
rule  for  expressing  this  relation. 

STEAM  TABLES  show  this  relation  as  well  as  the 
total  energy,  internal  and  external  work,  the  specific 
volume,  etc. 

SATURATED  STEAM  at  a  given  pressure  has  the 
temperature  and  specific  volume  given  in  the  steam 
tables  for  steam  at  that  pressure. 

SUPERHEATED  STEAM  is  steam  at  a  temperature 
higher  than  that  called  for  by  the  steam  tables  for 
steam  at  the  given  pressure. 


CHAPTER  VI 
FUNCTIONS  OF  A  STEAM  POWER  PLANT 

THIS  chapter  does  not  deal  with  the  design  or  with  the 
reasons  for  the  special  features  of  the  members  of  a  steam 
plant.  It  is  intended  rather  to  teach  the  student  the 
fundamental  functions  of  the  members  necessary  for  the 
operation  of  the  plant,  and  thus  to  show  the  reasons  for 
the  existence  of  the  members  themselves.  These  reasons 
for  existence  are  simple  and  should  be  thoroughly  under- 
stood before  the  student  attempts  to  study  the  details 
of  construction.  The  purpose  of  this  book  is  to  prepare 
the  reader  for  the  study  of  those  engineering  texts  which 
take  up  such  matters. 

50.  A  Simple  Plant.  The  whole  purpose  of  any  kind  of 
a  power  plant  is  to  get  energy  out  of  a  fuel  or  other  natural 
source  of  energy  and  to  transform  it  into  the  mechanical 
form.  In  the  steam  plant  the  supply  of  energy  is  in  the 
coal.  This  must  be  liberated,  carried  to  the  engine  cylinder 
and  then  transformed  into  mechanical  energy.  Thus  there 
are  three  distinct  processes  which  must  go  on:  first,  the 
burning  of  the  fuel  and  the  releasing  of  the  energy;  second, 
the  transporting  of  this  energy  to  a  place  where  it  can  be 
utilized;  and  third,  the  transforming  from  heat  energy  into 
mechanical  energy. 

In  every  kind  of  plant  there  must  be  the  following 
essential  parts  which  do  these  three  things: 

First.  A  furnace  in  which  energy  is  freed. 

Second.  A  boiler  where  the  heat  energy  is  delivered  to 

139 


140  HEAT 

water  and  where  steam  is  made.     The  steam  is  then  carried 
by  piping  to  the  third  essential  member. 

Third.  An  engine  where  the  energy  is  taken  out  of  the 
steam  and  given  to  a  fly-wheel  or  other  mechanical  parts. 
In  small  stationary  plants,  where  only  a  small  quantity  of 
energy  is  transformed,  no  additional  pieces  of  equipment 
are  commonly  used. 


FIG.  34. — Simple  Power  Plant  Operating  a  Hoist. 

Fig.  34  shows  a  familiar  type  of  portable  plant  in  which 
the  furnace,  boiler,  and  engine  are  all  mounted  on  a  common 
base.  Let  us  see  how  this  simple  plant  works. 

In  the  first  place  water  is  required  in  the  boiler  and  a 
supply  must  be  kept  there.  We  build  a  fire  in  the  furnace 
under  the  boiler  and  heat  the  water  until  it  boils  and  forms 
saturated  steam  over  the  water.  If  no  steam  is  being 
used,  the  continued  evaporation  or  boiling  of  the  water 


VI.     FUNCTIONS  OF  A  STEAM  POWER  PLANT    141 

causes  more  gas  (steam)  to  be  crowded  into  the  space  above 
the  water.  This  produces  an  increase  of  pressure.  When 
we  want  the  engine  to  deliver  work  (in  the  mechanical 
form)  we  turn  a  supply  of  hot  steam  under  pressure  into 
the  cylinder  of  the  engine.  This  cylinder  is  arranged  in  a 
way  similar  to  the  engine  shown  in  Figs.  35  and  36.  If 
the  engine,  when  the  steam  is  admitted,  stands  as  shown 
in  the  cut,  the  full  boiler  pressure  would  be  applied  to 
the  head  end  of  the  piston  and  only  the  atmospheric  pres- 
sure would  be  applied  to  the  crank  end  to  oppose  it.  The 
difference  between  the  pressures  on  the  two  sides  of  the 
piston  is  called  the  effective  pressure.  The  effective  pres- 
sure times  the  area  of  the  side  of  the  piston  against  which 
the  steam  is  pressing  measures  the  total  force  tending  to 
move  the  piston.  As  soon  as  the  piston  begins  to  move, 
the  engine  starts  to  do  work  and  then  the  conditions 
Become  more  complex. 

If  the  engine  runs  continuously  there  must  be  a  con- 
tinuous supply  of  coal  to  feed  the  fire,  of  water  to  feed  the 
boiler,  and  of  steam  to  feed  the  engine.  The  coal  is  the 
real  source  of  the  mechanical  energy  and  the  water,  boiler, 
piping,  steam,  and  steam  engine,  etc.,  are  all  machinery  to 
produce  the  transformation. 

As  the  piston  moves  from  one  end  of  the  cylinder  to  the 
other  it  makes  a  stroke.  The  pressure  during  the  stroke 
is  never  constant.  Therefore,  in  computing  the  work  done 
per  stroke  the  average  effective  pressure  for  the  entire  stroke 
is  always  used.  This  average  pressure  is  usually  called  the 
MEAN  EFFECTIVE  PRESSURE  (abbreviated  M.E.P.). 

The  work  in  ft.-lbs.  done  for  each  stroke  is  M.E.P.  in 
Ibs.  per  sq.in.Xpiston  area  in  sq. ins. X length  of  stroke  in 
ft.  In  a  typical  reciprocating  engine,  such  as  is  shown 
in  Fig.  35,  steam  is  admitted  to  both  ends  of  the  cylinder 
alternately.  Technically  we  describe  this  by  saying  that  an 
engine  is  double  acting  or  that  both  the  "  forward  stroke  " 
and  the  "  return  stroke  "  may  be  working  strokes.  The 


142 


HEAT 


engine  in  Fig.  35  is  making  the  " forward  stroke."  The  term 
"  forward  stroke  "  is  used  for  the  stroke  toward  the  crank. 
This  type  of  plant  is  necessarily  very  heavily  built  and 
roughly  adjusted,  to  stand  the  hard  usage  to  which  hoisting 
gear  is  commonly  subjected.  The  manufacturers  of  this 
type  of  plant  state  that  a  fair  day's  work  for  such  an 
installation  is  to  lift  9700  Ibs.  50  ft.  once  every  75  seconds 
of  a  ten-hour  working  day.  The  plant  which  does  this 
quantity  of  work  burns  on  an  average  a  ton  of  soft  coal 
each  day.  The  hoisting  gear  has  an  efficiency  of  80  per 


Fly  Wheel 


Crank  Shaft 
Bearin 


Piston 


FIG.  35. — Sectional  View  of  Steam  Engine  Cylinder, 

cent.     Assuming   13,600  B.T.U.  energy  per  pound  of  coal, 
the  efficiency  of  the  steam  plant  is  computed  as  follows: 


9700  Ibs.  X  50  ft. 


75 

—  min.X  33000  ft.-lbs.X80  per  cent 

ou 


15  H.P. 


15  H.P.  X 10  hours  =  150  H.P.  hours  per  day. 

Since,  according  to  the  manufacturers,  one  ton  of  coal  is 
used  per  day, 

2000-7-150  =  14.4  Ibs.  of  coal  per  H.P.  hour. 


VI.     FUNCTIONS  OF  A  STEAM  POWER  PLANT    143 


The  plant  efficiency  is 

B.T.U.  in  1  H.P.  hr. 
B.T.U.  in  14.4  Ibs.  coal"  14.4X13600 


2540 


=  .014  =  1.4  per  cent. 


In  this,  as  in  every  plant,  the  coal  which  is  supplied  is 
the  working  capital,  for  it  contains  the  heat  energy  from 
which  the  plant  must  be  run.  The  problem  is  to  conserve 
this  capital  and  make  the  greatest  possible  use  of  the 
available  supply. 

There  are  losses  at  every  step  in  the  series  of  processes 
which  we  have  described,  and  Fig.  37  shows  the  probable 


FIG.  36. — Steam  Engine  Parts. 

distribution  of  the  losses  in  this  particular  plant.  Very 
little  attention  has  been  given  to  investigating  and  report- 
ing in  detail  the  manner  in  which  all  of  this  energy  is 
lost  in  the  type  of  plant  shown.  However,  the  figures 
given  are  a  probable  approximation. 

The  energy  in  14.4  Ibs.  of  coal  is  represented  in  Fig.  37 
as  passing  in  a  stream,  first  through  the  furnace,  next  after 
sustaining  losses,  through  the  boiler  and  finally  through  the 
engine.  The  width  of  the  stream  represents  to  scale  the 
amount  of  the  energy  at  each  point  along  the  stream.  The 
losses  are  indicated  by  showing  a  part  of  the  stream  as 
diverted  aside. 

The  surprising  fact  which  this  figure  and  the  preceding 
computation  show  is  that  only  1.4  per  cent  of  the  energy 


144 


HEAT 


68,000  B.T.U.  In  exhaust,    Drip  Wasted 
starting  and  stopping,  etc. 

2000  B.T.U.     Radiation 


92,000  B.T.U.      Up   stack 
In  hot  gases. 


9.000  B.T.U.     Radiation. 
Leakage,  etc. 


1,000  B.T.U.     Radiation 
about  Firebox. 


21.000  B.T.U.  Due 
to  coal  In  ash  and  incom- 
plete Combustion. 


ENGINE 


BOILER 


FURNACE 


FIG.  37. — Energy  Diagram  for  the  Plant  in  Fig.  34. 


VI,      FUNCTIONS  OF  A  STEAM  POWER  PLANT     145 

in  the  coal  was  used  for  useful  work.  In  small  plants  of 
this  sort,  people  waste  a  large  part  of  the  coal  rather  than 
go  to  the  expense  of  improving  the  equipment  and  use  the 
labor  to  operate  improved  equipment  economically.  In 
technical  language  this  idea  is  expressed  by  saying  that 
in  spite  of  the  apparently  low  fuel  economy,  a  higher  cost 
economy  results  than  would  be  obtained  with  improved 
equipment. 

Problem  1.  What  would  be  the  thermal  efficiency  of  the 
engine  in  the  plant  referred  to  in  Fig.  37? 

Problem  2.  What  would  be  the  efficiency  of  the  boiler  and 
furnace  in  Fig.  37  expressed  in  the  number  of  pounds  of  water  it 
could  evaporate  from  and  at  212°  F.  per  pound  of  coal  burned? 

Problem  3.  What  per  cent  of  energy  delivered  to  the  furnace 
is  transmitted  in  the  steam  to  the  engine  in  Fig.  37? 

Problem  4.  If  we  define  a  boiler  H.P.  as  34.5  Ibs.  of  water 
evaporated  from  and  at  212°  F.  (A.S.M.E.  rating)  what  is  the 
H.P.  of  the  boiler  in  Prob.  2? 

Problem  5.  In  Fig.  37  we  have  accounted  for  the  work  done 
in  raising  the  load  vertically.  Suppose  that  75  per  cent  of  the 
engine's  output  was  consumed  while  the  load  was  being  raised 
vertically  and  that  an  additional  25  per  cent  was  used  while  the 
load  was  being  moved  horizontally.  Reconstruct  the  energy  dia- 
gram, distributing  the  losses  to  furnace,  boiler,  and  engine  in 
the  same  proportion  as  in  Fig.  37. 

Problem  6.  A  steam  power  plant  uses  8  tons  of  coal  contain- 
ing 14,000  B.T.U.  per  pound  per  ten-hour  day.  It  converts 
110,000  Ibs.  of  water  from  70°  F.  to  steam  at  160  Ibs.  What  is 
the  efficiency  of  the  boiler  and  furnace  in  terms  of  pounds  of  coal 
per  boiler  H.P.  hour?  (Use  A.S.M.E.  rating.) 

Problem  7.   Give  the  thermal  efficiency  in  per  cent  in  Prob.  6. 

Problem  8.  If  the  plant  in  Prob.  6  averages  throughout  the 
day  to  deliver  600  B.H.P.,  what  is  the  over-all  plant  efficiency 
in  per  cent? 

Problem  9.  Give  efficiency  in  Prob.  8  in  pounds  of  coal  per 
H.P.  hour. 

Problem  10.  If  there  is  8  per  cent  waste  in  coal  (92  per  cent 
combustible)  give  pounds  of  combustible  per  H.P.  hour. 

51.  Circulation  of  Water,  etc.  In  a  plant  rated  at  1000 
H.P.,  or  more,  attention  is  given  to  eliminating  losses  and  to 


146 


HEAT 


increasing  the  fuel  efficiency  of  the  various  members  of  the 
steam  plant.     The  plant  as  a  whole  is  run  at  a  saving  of 


SURFACE  CONDENSER 

FIG.  38.— Water  Circulation  in  Typical  Plant. 

coal  by  the  introduction  of  members  not  yet  described. 

Fig.  38  shows  the  water  circulation  in  a  plant  large  ?nough 

to  make  it  profitable  to  employ  economizers,  superheaters, 


VI.     FUNCTIONS  OF  A  STEAM  POWER  PLANT    147 


Radiation 


«-2MO  Useful  Work 
160  Engine  Friction 


Leakage  and  Radiation    500 
from  Boiler  Setting 

Radiation  from  Boiler      600 


To  Run  Feed  Pamps,  Air  Pumps 
and  other  auxilaries 


To  Flue 


FIG.  39.— Energy  Diagram  for  Plant  of  Fig.  38 


148  HEAT 

and  condensers,  with  the  necessary  feed  pumps,  air  pumps, 
blowers,  etc. 

It  will  be  noticed  that  water  is  forced  into  the  economizer 
by  the  feed  pump.  The  water  in  the  economizer  is  at  the 
boiler  pressure  and  consequently  passes  into  the  boiler  in 
a  steady  stream  as  fast  as  it  is  supplied  by  the  feed  pump. 
The  boiler  changes  the  water  into  steam  and  the  steam  passes 
from  the  steam  dome  to  the  superheater  on  its  way  to  the 
engine.  The  steam  is  still  practically  at  boiler  pressure. 
The  engine  takes  small  quantities  of  the  steam  at  each 
stroke  and  expands  the  steam  in  its  cylinders  down  to  a  low 
pressure.  This  steam,  which  may  be  exhausted  at  less  than 
1  Ib.  pressure,  contains  a  large  amount  of  moisture,  and  the 
mixture  of  steam  and  water  is  passed  into  the  condenser. 
The  wet  vacuum  pump,  shown  at  the  lower  left-hand  side  of 
the  condenser,  maintains  the  vacuum  in  the  condenser  and 
also  pumps  the  water  out  of  it.  This  water  may  now  be 
used  as  supply  water  for  the  feed  pump  and  circulated 
through  the  economizer,  boiler,  engine,  and  condenser  an 
indefinite  number  of  times.  Except  for  leakage  no  loss  of 
water  takes  place  in  such  a  system. 

It  will  be  noticed  that  there  is  a  separate  water  cir- 
culating system  used  to  keep  the  condenser  cool.  By 
carefully  examining  the  surface  condenser,  the  student  will 
see  that  the  "  injection  water"  is  pumped  by  the  pump 
at  the  lower  right-hand  side  through  an  independent  set 
of  piping.  The  water  is  forced  in  at  I  and  out  at  D 
without  coming  in  contact  with  the  steam.  The  water 
rises  from  I  to  D  but  the  steam  falls  from  E  to  A.  Thus 
it  will  be  seen  that  these  currents  run  in  opposite  direc- 
tions. We  say  that  the  apparatus  acts  upon  the  counter- 
current  principle. 

The  flow  of  gases  should  also  be  observed  from  Fig.  38. 
It  should  be  remembered  that  the  air  after  passing  through 
the  fire-bed  and  supporting  combustion  becomes  very  hot, 
and  is  changed  in  chemical  composition.  The  resulting  hot 


VI.      FUNCTIONS  OF  A  STEAM  POWER  PLANT     149 

gaseous  products  pass  over  the  head  ends  of  the  water 
tubes.  After  delivering  a  portion  of  their  heat  energy,  the 
gases  reach  the  superheater.  As  indicated  by  the  arrows, 
the  gases  are  deflected  by  the  baffle  plate  after  heating  the 
superheater  tubes,  pass  down  over  the  boiler  tubes  again 
and  are  made  to  pass  up  over  the  water  tubes  a  third  time 
before  entering  the  economizer.  From  the  economizer  the 
gases  pass  up  the  stack. 

52.  Energy  Circulation.  To  study  the  way  in  which  the 
energy  in  the  fuel  is  transformed  to  mechanical  energy  by 
the  plant,  let  us  examine  Fig.  39. 

An  attempt  is  here  made  to  find  what  becomes  of  the 
energy  from  1.6  Ibs.  of  coal  containing  a  total  of  20,160 
B.T.U.,  as  a  test  showed  that  this  was  the  average  weight 
required  per  H.P.  hour.  The  energy  is  represented  as  a 
stream  which  is  considered  to  be  passing  from  the  coal 
through  the  firebox,  superheater,  boiler,  etc.  As  has  been 
stated,  the  superheater  in  this  case  was  inside  the  boiler 
setting,  but  for  purposes  of  analysis  it  was  thought  best  in 
this  diagram  to  consider  the  boiler  and  superheater  as 
being  separate  members. 

As  in  Fig.  37  the  width  of  this  stream  represents  to 
scale  the  relative  amounts  of  energy  flowing  through  each 
part  of  the  plant  and  losses  are  shown  by  indicating  that  a 
part  of  the  stream  has  been  diverted  to  one  side. 

The  energy  is  released  in  the  furnace,  but  the  process 
is  not  complete  and  a  certain  amount  of  coal  is  dropped 
into  the  ashpit  and  wasted.  100  RT.U.  are  shown  to  be 
lost  thus.  The  steam  in  the  superheater  is  shown  to  gain 
610  B.T.U.  by  being  superheated  100°  F.  above  the  boiler 
temperature.  The  superheater  is  not  shown  as  having  any 
losses,  as  all  of  the  radiated  heat  is  available  for  the  boiler, 
since  the  superheater  is  in  the  boiler  setting.  The  boiler, 
however,  and  the  boiler  setting  (which  is  really  part  of  the 
furnace)  are  charged  with  a  total  loss  of  1100  B.T.U. ,  due 
to  radiation  and  leakage.  Some  of  the  steam  generated 


150  HEAT 

in  the  boiler  miist  be  used  to  run  auxiliaries  such  as  pumps, 
blowers,  etc.,  and  therefore  must  be  charged  up  to  the 
plant  as  a  loss. 

After  the  products  of  combustion  pass  out  of  the  boiler 
setting  into  the  economizer,  they  still  contain  5650  B.T.U. 
of  heat  energy.  500  B.T.U.  are  shown  as  lost  in  radiation 
and  2520  B.T.U.  are  shown  as  going  up  the  flue  and  serving 
no  useful  purpose  except  as  they  contribute  to  the  draft. 
The  economizer  saves  2630  B.T.U.  which  would  otherwise 
go  up  the  flue.  This  energy  stream  is  carried  back  to  the 
boiler  as  the  feed  pump  forces  the  water  through  the  econo- 
mizer to  the  boiler.  As  the  water  drawn  from  the  condenser 
is  somewhat  warmer  than  tap  water,  610  B.T.U.  are  shown 
to  be  saved  by  using  the  water  from  the  condenser  over  again. 
This  saving  is  from  the  energy  thrown  into  the  condenser  by 
the  engine.  The  total  saving  by,  the  economizer  is  therefore 
610+2630  =  3240  B.T.U.,  which  is  returned  to  the  boiler. 

In  the  boiler  the  water  is  changed  to  steam.  Some  01 
the  steam  is  used  in  the  auxiliaries  and  for  service  purposes 
about  the  boiler  house.  The  greater  part  of  the  steam  is 
delivered  to  the  superheater  and  passes  on  to  the  engine. 
In  the  superheater  the  610  B.T.U.  already  referred  to  are 
taken  up  to  raise  the  temperature  above  that  of  saturated 
steam  at  235  Ibs.  pressure. 

In  this  analysis  it  was  assumed  that  the  steam  was  dry 
when  it  came  from  the  boiler.  If  the  quality  of  the  steam 
was  poor  (that  is,  if  the  steam  contains  some  water)  the 
superheater  supplied  some  of  the  energy  shown  in  the 
diagram  as  supplied  by  the  boiler.  This  very  likely  was 
the  case,  but  when  the  quality  is  very  good  (or  as  we  some- 
times say,  when  the  quality  is  nearly  1)  it  is  not  easy  to 
detect  the  small  amount  of  water  present.  If,  however, 
the  quality  had  been  995,  it  would  have  required  .5  per  cent 
of  the  latent  heat  at  235  Ibs.  to  evaporate  this  moisture. 
To  each  pound  of  steam  used  the  superheater  would  have 
then  added  (.005X827)  =4,1  B.T.U.  additional. 


VI.     FUNCTIONS  OF  A  STEAM  POWER  PLANT     151 

The  engine  is  seen  to  have  an  energy  stream  of  15,080 
B.T.U.  flowing  in.  Of  this,  it  loses  in  radiation  300  B.T.U. 
and  throws  into  the  condenser  12,070  B.T.U.  2540  B.T.U. 
(or  1  H.P.  hour)  have  appeared  as  useful  work  or  energy 
in  the  mechanical  form  at  the  fly-wheel.  There  was  an 
additional  amount,  150  B.T.U.,  of  mechanical  energy  trans- 
formed which  was  used  up  in  overcoming  the  friction  of  the 
moving  parts  of  the  steam  engine. 

This  energy  (2540  B.T.U.)  is  delivered  at  the  fly-wheel 
and  could  be  measured  with  a  Prony  brake  or  other  suitable 
means.  The  indicated  horse-power  (I.H.P.),  however,  is 
not  available  from  the  data  given  in  the  figure.  The  I. H.P. 
is  the  actual  rate  of  delivering  mechanical  energy  to  the 
piston  and  is  obtained  by  finding  the  M.E.P.  by  means  of  a 
Watts  Indicator  (see  Chapter  XI),  Then 


Force  in  Ibs.  X  distance  in  ft.  per  Min. 

Power=__    33000ft.lbs- 


For  the  forward  stroke  I.H.P.  = 

M.E.P.  X  Area  piston  in  sq.in.  XR.P.M.  XLength  stroke  in  ft. 

33000  f t.-lbs.  1 

or  more  briefly: 


Forward  Stroke  I.H.P.= 


force  distance 

(M.E.P.  X  A)  X  (R.P.M.  XL) 
33000  ft.-lbs. 


If  the  engine  is  double  acting,  care  must  be  taken  to 
obtain  the  M.E.P.  for  both  ends  and  to  make  correction  for 
the  cross-section  area  of  the  piston  rod  on  the  crank  end 
of  the  piston.  It  is  best  to  compute  I.H.P.  developed 
by  each  end  and  add  the  power  from  each  end  to  get  the 
total  I.H.P.  Thus 


152  HEAT 

Return  stroke  I.H.P.  = 

(M.E.P.  crank  endXArea  crank  end)X(R.P.M.XL) 
33,000  ft.-lbs. 

and 

Total  I.H.P.=  Forward  I.H.P. +Return  I.H.P. 

The  difference  between  the  I.H.P.  and  the  B.H.P.  is 
the  power  lost  in  the  engine.  This  loss  is  due  to  the 
friction  of  the  piston,  and  the  friction  of  the  various 
bearings.  Part  of  the  energy  used  to  overcome  friction  is 
at  once  converted  back  into  heat  within  the  cylinder  and  is 
carried  off  in  the  exhaust  or  by  radiation  from  the  surface. 
Because  this  information  is  not  shown  in  the  energy 
diagram  (Fig.  39)  the  I.H.P.  cannot  be  computed  in  this 
case. 

The  mixture  of  water  and  steam  is  exhausted  from  the 
engine  into  the  condenser.  In  the  figure,  a  surface  type 
of  condenser  is  shown  and  in  this  type  the  exhaust  passes 
down  over  the  outer  surface  of  successive  layers  of  piping 
containing  cold  circulating  water.  The  steam  and  the 
circulating  water  do  not  mix  at  all,  but  the  steam  gives  up 
its  latent  heat  to  the  pipes  kept  cold  by  the  water.  This 
condenser  is  like  that  shown  in  Figs.  44  and  45. 

The  condensed  water  in  the  case  under  discussion  is 
pumped  out  by  an  air  pump  (sometimes  called  wet  vacuum 
pump)  and  is  then  available  to  be  fed  again  to  the  boiler. 

53.  The  Energy  Stream  is  seen  to  flow  on  steadily 
through  each  member  of  the  steam  plant.  It  is  the  aim 
of  both  the  designing  engineer  and  the  operating  engineer 
to  see  that  the  least  possible  amount  of  energy  is  lost  in 
each  member.  There  has  been  a  constant  study  of  all  the 
details  of  the  construction  and  operation  of  steam  power 
plants  to  this  end.  Through  the  invention  of  new  processes 
of  manufacture,  new  materials,  new  improvements  in  design, 
and  the  increase  in  the  size  of  the  plants  and  of  the  engine 


VI.     FUNCTIONS  OF  A  STEAM  POWER  PLANT     153 

units,  the  possibilities  of  great  improvement  in  the  existing 
types  of  steam  plants  have  been  exhausted.  The  best  that 
can  be  done  is  to  study  each  member,  determine  the  cost 
of  coal,  and  the  other  cost  relations  for  the. town  where 
the  plant  is  situated  and  select  the  type  of  equipment  and 
plan  of  operation  which  gives  the  lowest  operating  cost. 

Problem  11.  What  per  cent  of  energy  entering  the  engine  of 
Fig.  39  appears  as  useful  work? 

Problem  12.  What  per  cent  of  the  energy  in  the  coal  is  turned 
into  useful  mechanical  energy  by  the  plant  under  discussion  in 
Fig.  39? 

Problem  13.  What  per  cent  of  energy  available  for  the  super- 
heater, boiler,  and  furnace  was  not  wasted  in  Fig.  39? 

Problem  14.  What  per  cent  of  the  energy  in  the  coal  was 
saved  by  the  superheater?  (Fig.  39.) 

Problem  15.  What  was  the  weight  of  water  used  by  the  engine 
per  B.H.P.  hour,  if  the  water  from  the  economizer  was  at  200°  F.? 
(The  water  rate  is  usually  the  weight  of  water  per  I.H.P.  hour.) 

Problem  16.  Assuming  the  steam  delivered  by  the  boiler  to 
be  dry,  how  many  degrees  was  the  steam  superheated  in  Fig.  39? 

Problem  17.  From  the  data  in  Fig.  37  compute  what  per 
cent  of  the  energy  in  the  coal  is  available  for  steam  heating, 
if  the  exhaust  steam  is  piped  into  a  building?  WThat  per  cent 
in  Fig.  39? 

Problem  18.  If  15  Ibs.  of  water  at  80°  F.  per  B.H.P.  hour  was 
circulated  through  the  economizer  in  Fig.  39,  what  was  the  boiler 
feed-water  temperature? 

Problem  19.  If  the  auxiliaries  of  the  steam  plant  in  Fig.  39 
use  on  the  average  80  Ibs.  of  saturated  steam  per  B.H.P.  hour 
developed,  and  if  the  total  weight  of  water  evaporated  by  the 
boiler  per  hour  was  15,000  Ibs.,  what  B.H.P.  was  being  developed 
by  the  various  auxiliaries  of  this  plant?  - 

Problem  20.  If  the  injection  water  in  the  condenser  of  the 
plant  shown  in  Fig.  39  was  at  a  temperature  of  56°  F.  and  the 
discharge  at  80°  F.,  what  weight  of  water  must  be  circulated  if 
15,000  Ibs.  of  steam  per  hour  was  evaporated,  the  auxiliaries 
were  run  as  a  condensing  engine,  and  the  total  weight  was  thrown 
in  at  El  (Assume  that  the  diagram  is  worked  out  for  15  Ibs.  of 
steam.) 

Problem  21.  If  the  auxiliaries  in  Prob.  20  had  been  run  non- 
condensing  what  would  have  been  the  weight  of  water  required? 


154 


HEAT 


It  is  not  the  object  of  this  chapter  to  teach  the  details 
of  construction  of  each  common  device  or  member  of  the 
steam  plant.  The  foundation  of  theory  which  will  help 
the  student  in  the  use  of  other  books  is  all  that  space  will 
allow.  A  few  members  and  types  are  discussed  by  way 
of  illustration. 

54.  The  Steam  Boiler.  A  typical  boiler  is  shown  in 
Fig.  40,  and  the  student  is  requested  to  notice  that  the 


FIG.  40. — Babcock  and  Wilcox  Boiler  with  Mechanical  Stoker. 

water  drops  down  the  back  water  leg  M  and  rises  in  the 
inclined  water  tubes  to  the  front  header  B.  As  the  water 
circulates  it  takes  up  heat  energy  from  the  furnace  and 
thus  some  of  the  water  is  evaporated  before  entering  the 
front  header  B.  The  presence  of  steam  in  the  water  makes 
the  mixture  of  water  and  steam  weigh  much  less  per  unit 
volume  in  the  front  end  of  the  tubes  than  in  the  back 
water  leg,  and  this  difference  in  weight  causes  the  convec- 
tion currents  or  the  circulation  of  the  water. 


VI.     FUNCTIONS  OF  A  STEAM  POWER  PLANT    155 

In  Fig.  41  is  shown  a  Sterling  boiler.     This  is  a  quick- 
steaming  type,  because  it  holds  less  water  per  rated  H.P. 


FIG.  41. — Sterling  Boiler  with  Mechanical  Stoker. 

There  are  three  so-called  steam  drums  at  the  top  and  a 
mud  drum  at  the  bottom,  but  the  amount  of  water  carried 


156  HEAT 

by  the  four  is  much  smaller  than  in  the  boiler  shown  in 
Fig.  40.  Baffles  are  placed  behind  the  first  and  second 
banks  in  such  a  way  as  to  compel  the  gaseous  products  of 
combustion  to  pass  first  over  the  first  bank  of  tubes,  second, 
through  the  superheater  and  down  between  the  tubes  of  the 
second  bank;  third,  up  along  the  third  bank. 

As  has  already  been  stated,  it  is  usual  to  define  a 
BOILER  HORSE-POWER  as  the  capacity  to  evaporate  34.5 
Ibs.  of  water  at  212°  F.  to  steam  at  212°.  However, 
steam  is  seldom  made  under  these  conditions,  and  so  it  is 
necessary  to  compute  the  equivalent  evaporation  from  and 
at  212°  F.  for  each  set  of  conditions  met.  If  steam  at 
constant  pressure  is  being  generated  from  feed  water  at 
constant  temperature,  the  heat  per  pound  of  water  added 
by  the  boiler  will  be  constant.  The  ratio  between  this 
quantity  and  the  heat  necessary  to  evaporate  from  and 
at  212°  F.  is  also  a  constant,  and  is  called  the  FACTOR 
OF  EVAPORATION.  This  factor  is  useful  in  computing  the 
results  of  boiler  tests. 

Factor  of  Evaporation  = 

Total  heat  in  steam  — total  heat  in  feed  water 
970 

where,         Total  heat  in  steam  =  latent  heat  at  boiler  press- 
ure X  quality + sensible  heat 
(see  Steam  Tables) ; 
Total  heat  in  feed  water  =  sensible  heat  of  the  feed 

water  as  it  enters  boiler; 
970  =  latent  heat  at  212°  F. 

Problem  22.  In  a  given  boiler  test,  water  was  fed  at  170°  and 
99  per  cent  quality  steam  at  190  Ibs.  gauge  was  delivered  by 
the  boiler.  Find  the  Factor  of  Evaporation. 

Total  heat  in  feed  water  above  32° 138  B.T.U. 

Total  heat  in  steam  at  205  Ibs.  gauge 1198  B.T.U. 

Latent  heat  of  steam  at  205  Ibs.  pressure  or  at  383°  F .     842  B.T.U. 


VI.      FUNCTIONS  OF  A   STEAM  POWER  PLANT     157 

If  1  per  cent  of  the  original  water  is  not  yet  evaporated  but 
is  floating  as  a  mist  in  the  steam  at  220  Ibs.  absolute  pressure, 
the  total  energy  will  be  less  than  given  in  the  steam  table  by 
1  per  cent  of  the  latent  heat,  or 

8.4  B.T.U. 
Heat  contributed  by  the  boiler 

(1198-8.4-138)  =1052  B.T.U. 

Factor  of  Evaporation  =  ~-    =  1 .085. 

y  i\) 

55.  The  Efficiency  of  a  Steam  Boiler  is  the  technical 
name  commonly  used  for  the  combined  efficiency  of  the 
boiler,  furnace,  and  grate. 

The  practice  in  the  numerical  computation  varies. 
Properly  the  combined  efficiency  of  a  grate,  furnace,  and 
boiler  should  be  the  quotient  of  the  energy  in  the  steam  added 
and  delivered  by  the  boiler,  divided  by  the  total  energy  in  the 
fuel  stoked.  In  this  case  the  energy  in  the  steam  would 
be  computed  by  multiplying  the  weight  of  steam  delivered 
by  the  difference  between  the  total  heat  in  the  steam  and 
the  heat  in  the  feed  water. 

_.   .,      „_  .  added  B.T.U.  delivered  in  steam 

Boiler  Efficiency  =  —         — n  ^  TT   . —  — . 

B.T.U.  in  coal. 

For  purposes  of  comparison  of  boiler  performance  it  is 
usual  to  compute  the  heat  energy  transmitted  to  the  water, 
and  divide  this  quantity  by  the  weight  of  combustible. 
(Heat  energy  transmitted  to  the  water  is  equal  to  the  water 
evaporated  per  pound  X  heat  gained  per  pound  in  the  boiler. 
The  weight  of  combustible  is  the  total  weight  of  fuel  minus 
the  weight  of  ash  and  coal  taken  from  ashpit.)  This 
quantity  is  sometimes  called  the  efficiency  of  the  boiler 
or  FUEL  EFFICIENCY.  Often  the  efficiency  is  stated  in 
terms  of  the  pounds  of  steam  delivered  per  pound  of  com- 


158  HEAT 

bustible  burned,  but  it  may  more  properly  be  called  the 
combined  efficiency  of  the  furnace  and  boiler.  Instead  of 
using  the  weight  of  the  combustible  in  the  coal  to  compute 
the  FUEL  EFFICIENCY,  frequently  the  weight  of  steam  per 
pound  of  fuel  as  stoked  is  given.  The  weight  of  steam  is 
usually  the  equivalent  weight  which  could  be  evaporated 
from  and  at  212°  F.,  but  the  computation  and  results 
must  be  inspected  each  time  to  be  sure  of  them.  The 
steam  tables  in  use  previous  to  1911  have  values  differing 
from  those  given  in  Marks  &  Davis'  steam  tables,  and 
in  the  1911  edition  of  Peabody's  steam  tables  by  as  much 
as  .5  per  cent  in  some  cases. 

The  Water  Rate  is  usually  computed  as  the  pounds  of 
steam  and  water  per  I.H.P  hour  passing  through  the 
cylinder.  It  is  sometimes  computed  on  a  B.H.P.  hour 
basis  or  a  Kw.  hour  basis. 

All  of  these  irregularities  in  the  practice  of  engineers 
reporting  tests  require  that  the  data  from  tests  be  inspected 
with  care  to  determine  just  what  the  results  mean.  The 
student  should  always  go  back  of  the  "  label "  or  term  used 
and  see  that  the  author  means  the  same  thing  that  the 
student  has  been  taught  is  good  usage.  The  student  must 
be  prepared  to  convert  results  expressed  in  any  of  the 
ways  indicated  to  equivalent  results  under  any  other  set 
of  conditions.  Only  in  this  way  can  valuable  results  for 
comparison  be  obtained. 

In  Appendix  E  will  be  found  the  recommendations  as 
to  the  use  of  these  terms  given  in  the  Preliminary  Report 
of  the  Power  Test  Committee  Code  of  1912. 

Problem  23.  If  the  feed-water  temperature  in  Fig.  39  had 
been  240°  F.,  what  would  have  been  the  equivalent  evaporation 
from  and  at  212°  F.? 

Problem  24.  In  Fig.  39,  if  the  feed-water  temperature  was 
injected  at  70°  F.  and  the  steam  pressure  was  80  Ibs.  gauge,  how 
much  water  per  pound  of  coal  was  evaporated  by  the  boiler? 

Problem  25.     In  Fig.  39  what  was  the  evaporation  of  water 


VI.  FUNCTIONS  OF  A  STEAM  POWER  PLANT  159 

per  pound  of  coal  from  and  at  212°  F.  if  the  water  left  the  econo- 
mizer at  215°  F.? 

Problem  26.  What  was  the  Factor  of  Evaporation  in  Problem 
23? 

Problem  27.  What  was  the  Factor  of  Evaporation  in  Problem 
24? 

Problem  28.  How  much  water  could  the  boiler  in  Fig.  39 
evaporate  if  its  efficiency  were  not  changed,  if  the  boiler  feed- 
water  temperature  was  80°  F.  and  the  steam  pressure  was  75  Ibs. 
gauge? 

Problem  29.  If  sample  10  in  Table  IV  were  burned  under  a 
boiler,  whose  combined  efficiency  with  the  furnace  was  75  per 
cent,  if  the  feed-water  temperature  was  85  per  cent  and  if  the 
boiler  pressure  was  200  Ibs.  gauge,  what  weight  of  water  would 
be  evaporated? 

Problem  30.  If  the  quality  of  the  steam  was  98.5  as  it  was 
drawn  from  the  boiler  in  Problem  28,  what  weight  of  water  would 
be  evaporated? 

Problem  31.  If  in  Fig.  39,  the  boiler  feed  water  entered  at 
200°  F.  and  at  the  rate  of  15,000  Ibs.  of  water  per  hour,  how  many 
B.H.P.  (A.S.M.E.  rating)  were  the  boilers  and  superheaters 
developing? 

Problem  32.  If  the  coal  used  in  Fig.  39  contained  14  per  cent 
of  waste,  and  the  boiler  feed  temperature  was  180°  F.,  what  was 
the  equivalent  evaporation  per  pound  of  combustible  from  and  at 
212°  F.? 


56.  Feed-water  Heaters  and  Economizers.  A  boiler 
shell  should  not  be  subjected  to  sudden  changes  of  tempera- 
ture, either  locally  or  as  a  whole.  The  resulting  contraction 
produces  serious  strains,  cracks,  and  sometimes  explosions. 
Therefore,  some  means  of  supplying  a  boiler  with  water 
at  approximately  boiler  temperature  is  a  very  important 
consideration.  For  large  plants  the  economizer  can  usually 
be  introduced  with  a  sufficient  saving  in  fuel  to  make 
the  large  investment  profitable.  An  ECONOMIZER  heats 
the  feed  water.  The  waste  gases  which  have  passed 
over  the  boiler  tubes  still  contain  considerable  heat  energy. 
They  are  made  to  pass  over  the  economizer  tubing  on  the 
way  to  the  chimney,  thus  giving  up  to  the  feed  water  a  part 


160 


HEAT 


of  this  energy  which  would  normally  be  wasted.  The  intro- 
duction of  an  economizer  makes  it  possible  for  the  boiler 
to  evaporate  a  larger  weight  of  water  per  hour.  Resistance 
is  added  to  the  flow  of  the  flue  gases,  but  usually  plants  have 
more  than  the  necessary  draft.  It  is  also  true  that  the 
fire  may  be  burned  at  a  considerably  faster  rate  with  econom- 
ical results,  (See  Fig.  42.)  When  the  engines  of  a  plant 


FIG.  42. — Green  Fuel  Economizer. 

are  run  non-condensing  it  is  generally  more  economical  to 
use  a  feed-water  heater.  A  FEED-WATER  HEATER  uses 
the  exhaust  steam  of  -  the  engines  as  its  source  of  heat 
energy.  In  Fig.  43  is  shown  a  type  in  which  the  exhaust 
steam  comes  in  direct  contact  with  the  water. 

In  either    case,   whether   the  feed  is   preheated   by   a 


VI.     FUNCTIONS  OF  A  STEAM  POWER  PLANT    161 


COLD  WATER 
SUPPLY 


EXHAUST 

OUTLET 


GRAVITV 
RETURNS 


WASTE: 


FIG.  43. — Cochran  Feed-water  Heater. 


162 


HEAT 


VI.      FUNCTIONS   OF  A   STEAM  POWER  PLANT     163 

>a 

feed-water  heater  or  an  economizer,  waste  energy  in  the 
form  of  flue  gases  or  exhaust  steam  is  utilized,  and  this 
accounts  for  the  fact  that  such  units  increase  the  efficiency 
of  steam  plants. 

57.  Condensers.      There  are  two  types  of  condensers, 


FIG.  45. — Sectional  View  of  Surface  Condenser  with  Air  and  Circulating 

Pumps. 

the  Surface  Condenser  and  the  Jet  ,,(or  Barometric)   Con- 
denser. 

Surface  Condenser.  This  condenser  is  like  that  shown 
in  Fig.  38  and  has  the  counter-current  circulation.  (See  the 
discussion  on  Page  148.)  This  counter-current  principle  is 
used  in  a  great  variety  of  industrial  processes.  Wherever  a 
heat  transfer  through  a  condenser  of  any  type  occurs, 
where  a  solute  is  interchanged  through  a  porous  membrane 
by  osmotic  pressure  (as  in  sugar  purification)  or  where 


164  HEAT 

fractional  distillation  is  being  performed,  it  is  used  with 
especial  frequency. 

The  steam  is  hot  at  the  top  and  after  being  condensed 
to  water  trickles  over  the  pipes  to  the  bottom  and  grad- 
ually cools  to  approximately  the  temperature  of  the  pipes 
at  the  bottom.  The  cold  water  enters  at  the  bottom,  where 
it  first  comes  in  contact  with  the  coldest  condensed  water 
and  tends  to  absorb  some  of  its  sensible  heat.  Warmed 
by  this  small  quantity  of  energy  it  rises  to  pipes  in  contact 
with  the  steam,  where  it  receives  the  relatively  large  quantity 
of  latent  heat  which  the  steam  must  give  up.  The  circulat- 
ing water  is  discharged  at  the  top,  from  which  point  it  may 
be  pumped  to  a  cooling  tower  and,  after  being  sprayed  over 
lattice  work  and  cooled  by  the  evaporation  of  part  of  it  in 
the  air,  the  remainder  may  be  injected  again  into  the  con- 
denser. In  coast  towns  and  on  shipboard  the  water  which 
is  injected  into  the  condenser  may  be  drawn  from  the  ocean 
and  the  hot  discharge  water  which  leaves  the  top  of  the 
condenser  allowed  to  flow  back.  If  the  plant  has  a  plen- 
tiful supply  of  artesian  well  water,  the  cooling  tower  is 
unnecessary. 

The  primary  advantage  of  using  a  condenser  in  a  steam- 
power  plant  lies  in  the  fact  that  the  condenser  reduces  the 
back  pressure  upon  the  engine.  When  a  condenser  is  used 
the  amount  of  the  back  pressure  in  pounds  per  square  inch 
is  numerically  determined  by  subtracting  the  vacuum 
expressed  in  inches  of  mercury  from  the  barometer  reading 
and  dividing  by  2.04. 

Jet  Condenser;  Fig.  46,  shows  the  water  circulation  in 
a  plant  served  by  a  jet  or  barometric  condenser.  A  dry- 
vacuum  pump  is  piped  to  the  top  of  the  mixing  chamber 
at  F.  Water  is  pumped  up  to  a  level  from  which  the 
vacuum  in  the  chamber  can  draw  or  siphon  it  the  remainder 
of  the  way  into  the  mixing  chamber. 

Fig.  47  shows  both  a  cut-away  section  and  a  sectional 
drawing  of  the  barometric  condenser  of  Fig.  46.  The 


VI.      FUNCTIONS  OF  A  STEAM  POWER  PLANT     165 

circulating  water  enters  at  B  and  impinges  upon  the  cone  C, 
which  causes  the  column  of  water  to  be  broken  into  a  spray. 
Exhaust  steam  enters  at  A  and  coming  in  contact  with  the 
spray  is  quickly  condensed.  The  bottom  of  the  chamber  H 
is  piped  to  a  hot  well,  the  water  level  in  which  must  be  at 
least  35  ft.  lower  than  H  if  the  vacuum  is  to  be  main- 
tained. 

The  pipe  E  leads  a  portion  of  the  cooling  water  to  the 


NATURAL  DRAFT 
COOLING  TOWER 


COLO  WELL  OVERFLOW 


FIG.  46.— Section  of  Plant  Showing  Water  Circulation. 

large  space  in  the  head  of  the  condenser.  This  cools  the 
air  well  below  the  temperature  in  the  region  G,  H,  and 
greatly  reduces  the  weight  of  water  vapor  drawn  out 
through  F. 

An  incidental  advantage  resulting  from  the  use  of  a 
condenser  in  a  steam-power  plant  is  that  once  the  water 
has  been  evaporated  in  going  through  the  first  cycle  of 
operations  it  is  freed  from  the  salts  which  incrust  the  inner 


166 


HEAT 


surface  of  boilers  and  boiler  tubes  (and  form  boiler  scale) 
when  hard  water  is  fed  to  the  boiler. 

58.  Steam-engine  Functions.  All  heat  engines  are 
intended  to  produce  mechanical  motion  when  supplied  with 
a  compressed  gas.  As  a  first  principle  of  theory  we  may  say 
that  it  is  the  pressure  of  the  gas  upon  the  piston  of  a 
reciprocating  steam  engine  which  makes  it  move.  Of 
course,  the  reader  will  remember  that  it  is  really  the  differ- 
ence in  pressure  between  the  two  sides,  for  normally  there 
will  be  a  back  pressure  on  the  side  opposite  to  the  working 


FIG.  47. — Sectional  View  of  Alberger  Barometric  Condenser. 

fluid  due  to  the  atmospheric  pressure,  or  the  condenser 
pressure.  In  a  steam  turbine  we  must  have  the  gas 
under  pressure.  By  passing  the  gas  through  a  nozzle  it 
is  given  a  high  velocity.  A  good  mental  picture  will  be 
obtained  if  the  student  thinks  of  this  rapidly  moving  gas 
as  a  "  howling  hurricane "  blowing  through  a  greatly 
improved  type  of  enclosed  windmill.  Thus,  the  turbine, 
which  we  have  likened  to  a  windmill,  delivers  mechanical 
energy  with  approximately  the  same  efficiency  as  the  ordi- 
nary type  of  reciprocating  steam  engine.  Because  of  the 
absence  of  reciprocating  parts  the  turbine  is  an  extremely 


VI.     FUNCTIONS  OF  A  STEAM  POWER  PLANT    167 

convenient  type  of  engine.  For  driving  electrical  generators 
it  is  especially  desirable,  because  of  its  naturally  high  speed 
and  pure  rotary  motion. 

To  fully  discuss  the  relation  that  the  pressure  of  steam 
bears  to  its  energy  available  for  useful  work  in  an  engine 
requires  a  more  extended  study  of  the  relation  between  the 
temperature,  pressure,  volume,  and  quantity  of  heat  energy. 
Chapter  X  is  largely  devoted  to  a  discussion  of  this  topic, 
but  the  student  should  consult  a  text  in  Thermodynamics 
for  more  complete  information. 

The  most  essential  point  about  engine  theory  for  the 
practical  man  to  understand  is  that  the  useful  work  done 
by  any  steam  engine  must  be  taken  from  the  difference 
between  the  energy  in  the  steam  admitted  and  the  energy 
in  the  exhaust  steam.  Over  two-thirds  of  the  total  energy 
in  steam  above  32°  is  in  its  latent  heat.  It  is  evident,  there- 
fore, from  a  purely  theoretical  standpoint,  the  more  water 
in  the  exhaust  the  more  energy  has  been  left  in  the  engine. 

The  following  problem  is  worked  out  to  illustrate  this 
important  point.  Given  the  following  data: 

Pressure  in  steam  chest  of  engine 235  Ibs.  gauge 

Steam  exhausted  into  condenser  exerting  a 

total  back  pressure  of 1  Ib.  gauge 

Steam  admitted   and    exhausted  in    a  dry  and    saturated 
condition. 

Total  energy  per  Ib.  of  steam  admitted  (see 

steam  table) 1201  B.T.U. 

Total  energy  in  1  Ib.  of  steam  at  1  Ib.  (ex- 
haust) pressure 1104  B.T.U. 

Total  heat  energy  left  in  the  cylinder  under 

the  above  conditions  (1201-1104) 97  B.T.U. 

The  water  rate  for  this  engine  per  brake  H.P. 

hour  is  2540^97 26.2  Ibs. 

This  is  over  twice  as  much  steam  as  a  modern  engine 
would  use  under  such  conditions.  If  the  engine  in  this 


168  HEAT 

illustration  had  used  10  Ibs.  of  water  per  H.P.  hour  and 
there  were  no  losses  by  radiation,  leakage,  etc.,  in  the  engine, 
each  pound  of  steam  would  have  left  254  B.T.U.  in  the 
cylinder.  (254-97)  or  167  B.T.U.  of  this  energy  must  have 
been  latent  heat  of  the  water.  Since  the  heat  energy  of 
vaporization  for  1  Ib.  pressure  (gauge)  is  1034  B.T.U.,  there 
must  have  been  167-^-1034  or  16.1  per  cent  of  moisture  in 
the  exhaust  steam.  From  these  two  problems  it  follows 
that  the  more  efficient  an  engine  is,  the  greater  will  be  the 
percentage  of  moisture  in  the  exhaust. 

The  efficiencies  which  would  result  from  exhausting  dry 
saturated  steam  will  be  computed  in  the  following  instructive 
but  impractical  problems: 

Problem  33.  What  is  the  maximum  per  cent  of  energy  which 
could  be  transformed  by  a  steam-power  plant  having  a  boiler 
pressure  of  80  Ibs.  and  taking  feed  water  from  its  condenser, 
which  has  a  pressure  of  1  Ib.  absolute,  if  the  engine  received 
and  exhausted  dry  saturated  steam?  (Neglect  all  losses  due  to 
friction  of  engine,  condensation  in  cylinder  and  piping,  radiation, 
etc.)  . 

From  steam  table  we  will  see  that  under  1  Ib.  pressure  the 
exhaust  steam  and  consequently  the  condensed  feed  water  returned 
to  the  boiler  will  be  at  102°  F.  Steam  under  80  Ibs.  in  the  boiler 
will  be  at  312°  F.  and  have  a  total  heat  above  32°  F.  of  1177 
B.T.U.  We  must  subtract  from  this  the  heat  energy  already 
in  the  water  at  102°  F.  or  70  B.T.U.  total  heat  above  32°  F.  per 
Ib.  of  feed  water. 

/.  1177  B.T.U. -70  B.T.U.  =1107  B.T.U.,  the  heat  energy 
received  from  fuel. 

The  steam  exhausted  at  1  Ib.  pressure  has  a  total  heat  above 
32°  F.  of  11 13  B.T.U. 

Then  1177  B.T.U. -1113  B.T.U.  =64  B.T.U.  left  in  engine 

64 
cylinder,  or  output.    TTTT^  =  .0578  or  5.78  per  cent  converted. 

Problem  34.  W^hat  would  be  the  maximum  per  cent  of  trans- 
formation possible  if  the  plant  is  taking  feed  water  at  102°  F. 
and  exhausting  into  atmosphere,  under  conditions  expressed  in 
Prob.  33? 

Problem  35.     In  above  example,  what  would  be  the  maximum 


VI.     FUNCTIONS  OF  A  STEAM  POWER  PLANT     169 

per  cent  of  transformation  if  feed  water  were  taken  at  200°  F. 
and  engine  exhausted  into  the  atmosphere? 

Problem  36.  If  boiler  pressure  in  Problem  33  had  been  200 
Ibs.,  what  maximum  per  cent  of  transformation  would  have 
resulted? 

Problem  37.  If  boiler  pressure  in  Problem  34  had  been  200 
Ibs.,  what  maximum  per  cent  of  transformation  would  have 
resulted? 

59.  The  Rankine  Cycle  is  the  heading  under  which  is 
discussed  in  most  books  a  set  of  hypothetical  conditions 
which  are  assumed  to  exist  in  a  steam  engine.  In  speaking 
of  Fig.  38  it  was  made  clear  that  the  water  could  be  used 
over  and  over  again.  Each  time  a  given  pound  of  water  has 
completed  a  round  trip  through  the  apparatus  and  attained 
the  original  condition  we  say  it  has  completed  one  cycle. 
The  discussions  of  Carnot's  cycle,  and  Rankine's  cycle  both 
assume  ideal  conditions,  but  Rankine's  cycle  is  more 
directly  applicable  to  practical  engines  because  it  deals 
with  water  and  steam  as  the  working  medium  rather  than 
a  perfect  gas. 

In  the  Rankine  cycle  it  is  assumed  that  the  cylinder 
used  has  non-conducting  walls,  no  clearance,  no  leaks,  no 
friction,  and  is  in  every  way  perfect.  While  these  conditions 
cannot  exist  in  practice,  the  Rankine  cycle  fixes  the  limit 
of  perfection  toward  which  we  may  work  in  engine  design. 
In  discussing  the  indicator  cards  of  actual  engines,  engineers 
frequently  give  the  efficiency  of  the  engine  as  the  ratio 
between  the  I.H.P.  from  the  Watts  Indicator  Card  and 
the  ideal  horse-power  which  would  result  if  the  engine 
followed  the  Rankine  cycle. 

In  Fig.  48  we  have  an  ideal  indicator  card 'according  to 
the  Rankine  cycle.  Steam  is  admitted  to  the  cylinder  at 
a  temperature  TI  for  the  part  of  the  stroke  represented  by 
AB.  It  is  expanded  adiabatically  to  T<z  during  the  part 
of  the  stroke  represented  by  BC.  At  the  temperature  T% 
the  engine  exhausts  the  steam  against  the  back  pressure 
represented  by  PS.  The  condition  of  the  steam  when 


170 


HEAT 


taken  into  the  cylinder  is  represented  by  a  temperature  TI, 
pressure  Pi,  and  the  volume  V\.  The  condition  of  the 
steam  when  it  is  exhausted  into  the  condenser  is  repre- 
sented by  T2,  ¥3,  and  PS.  T2  is  also  the  temperature  of 
the  condenser.  If  the  extremely  small  amount  of  work 
required  to  return  the  water  from  the  condenser  to  the 
boiler  is  neglected,  the  efficiency  of  this  operation  is 
expressed  by  the  formula,  • 


FIG.  48. — Ideal  Indicator  Card  Following  Rankine  Cycle. 

where  HI  is  the  total  heat  energy  in  the  admitted  steam 
and  H2  is  the  total  heat  energy  in  the  steam  returned  to 
the  condenser.  Practically,  however,  the  HI  should  be 
denned  as  the  heat  energy  per  pound  added  by  the  steam 
boiler  and  the  H2  as  the  portion  of  HI  which  is  rejected  to 
the  condenser,  if  the  above  formula  is  to  give  the  efficiency 
of  a  perfect  steam  engine  using  the  steam  as  received  and 
delivered. 


VI.     FUNCTIONS  OF  A  STEAM  POWER  PLANT     171 

If  an  engine  drew  a  charge  of  a  perfect  gas  at  TI°  abso- 
lute, that  charge  would  have  an  amount  of  heat  represented 
by  KTi°,  where  K  depends  upon  the  weight  of  the  charge 
and  the  specific  heat,  which  are  assumed  to  remain  un- 
changed during  the  computation.  Similarly,  it  would  reject 
an  amount  of  heat  energy  equal  to  KT2°  if  T2°  is  the  tem- 
perature of  the  exhaust.  The  energy  left  in  the  cylinder 
equals  KTi°  —  KT2°  and  the  efficiency  is  the  useful  energy 
(energy  left  in  the  cylinder)  divided  by  the  total  energy 
taken  in,  or 

KTi°-KT2° 


Dividing  both  numerator  and  denominator  by  K,  we  have 

T1°—T2° 

Efficiency  =       m  0  —  . 
1  1 

The  ideal  efficiency  would  be  reached  when  adiabatic 
expansion  took  place  in  the  cylinder  of  the  engine  and  the 
gas  gave  up  as  much  energy  as  it  would  receive  when  under- 
going adiabatic  compression. 

If  it  is  assumed  that  a  perfect  gas  is  used  as  a  medium 
in  a  cycle  similar  to  Rankine's,  the  same  formula  will  express 
the  efficiency  of  a  perfect  heat  engine.  If  the  specific  heat 
of  the  gas  is  assumed  to  be  constant  the  total  heat  factors 
HI  and  Hz  are  in  direct  proportion  to  the  absolute  tem- 
peratures TI  and  T2  of  the  gas.  By  comparing  Figs.  56  and 
57  with  Fig.  48,  the  student  will  see  the  marked  difference 
which  exists  between  cards  which  are  taken  from  an  actual 
engine  and  an  ideal  card  following  the.  Rankine  cycle. 


172  HEAT 


REVIEW  PROBLEMS,  CHAPTER  VI 

38.  In  Fig.  30  what  per  cent  of  moisture  must  have  been 
required  per  H.P.  hour?  (assume  no  losses  except  those  shown). 

39.  If  in  Problem  38  the  steam  had  been  exhausted  into  the 
condenser  dry,    if  there  had  been    no    other   losses    than    those 
shown,  and  if  dry  saturated  steam  had    been  used,  how  much 
steam  would  have  been  required  per  H.P.  hour? 

40.  An  engine  uses  25  Ibs.  of  steam  per  H.P.  hour.     The 
steam  is  under  100  Ibs.  gauge  pressure;  quality  of  steam  990;  and 
steam  is  exhausted  into  the  atmosphere.    Assume  no  losses  or 
excess  back  pressure.    What  per  cent  of  moisture  must  there  be 
in  the  exhaust? 

41.  What  per  cent  of  energy  entering  the  engine  of  Fig.  62 
appears  as  useful  work? 

42.  What  per  cent  of  the  energy  in  the  coal  is  turned  into 
useful  mechanical  energy  by  the  plant  under  discussion  in  Fig.  62? 

43.  What  per  cent  of  energy  available  for    the  boiler  and 
furnace  was  not  wasted  in  Fig.  62? 

44.  A  boiler  receives  5200  B.T.U's.  per  minute  through  every 
square  feet  of  its  firebox  surface,  which  contains  54  sq.ft.     If  the 
boiler  temperature  is  287°  F.,  and  is  fed  with  condenser  water  at 
120°  F.}  what  weight  of  dry  steam  could  be  drawn  off  per  hour? 

46.  If  a  certain  boiler  vaporizes  30  Ibs.  of  water  per  hour 
from  a  feed- water  temperature  of  100°  F.,  into  steam  at  70  Ibs. 
gauge  pressure  for  every  boiler  horse-power  of  its  rating,  what 
per  cent  of  this  heat  in  the  boiler  does  the  rating  assume  to  be 
available  for  useful  work  (i.e.,  what  per  cent  engine  efficiency  does 
this  ratio  assume)? 

46.  Given  an  amount  of  heat  energy  equal  to  that  entering 
the  boiler  in  Problem  45,  how  many  pounds  of  water  per  horse- 
power would  be  vaporized  per  hour  from  a  feed-water  temperature 
of  212°  F.,  into  steam  at  14.7  Ibs.  pressure? 

47.  How  many  pounds  of  coal  per  rated  boiler  horse-power 
hour  would  be  required  by  boiler  in  Problem  45,  assuming  75  per 
cent  of  the  heat  given  off  by  burning  coal  goes  into  the  water? 

48.  Having  given  the  temperature  of  injection,  discharge,  hot 
well,  and  exhaust  steam,  as  50°,  100°,  120°,  and  150°  F.,  respect- 


VI.     FUNCTIONS  OF  A  STEAM  POWER  PLANT     173 

ively,  calculate  the  weight  of  water  required  to  condense  1  Ib.  of 
steam. 

49.  If  the  temperature  of  the  injection  is  70°  F.,  in  Problem  48, 
how  much  water  is  required? 

50.  350  Ibs.  of  coal  are  burned  on  a  boiler  grate  per  hour 
and  3000  Ibs.  of  water  are  passed  through  the  economizer,  the 
temperature  of  the  water  being  raised  150°  F.,  and  the  tempera- 
ture of  the  waste  gases  being  lowered  300°  F.     If  the  specific  heat 
of  the  flue  gases  is  .24,  what  weight  of  furnace  gases  are  produced 
per  pound  of  coal  burned? 

51.  An  engine  indicates  250  H.P.  with  a  steam  consumption 
of  18  Ibs.  per  I.H.P.  per  hour.     Having  given  the  following  tem- 
peratures, calculate  the  weight  of  injection  water  delivered  for 
each  double  stroke  of  the   circulating  pump,   which  is  making 
200  R.P.M. 

Temperatures  of  injection,  discharge,  hot  well,  and  exhaust 
steam,  55°,  110°,  125°,  and  138°  F.,  respectively. 

52.  If  25  Ibs.  of  circulating  water  are  required  for  each  pound 
of  exhaust  steam  condensed,  and  the  temperature  of  the  circulat- 
ing water  in  passing  through  the  tubes  is  increased  from  56°  to 
98°  F.,  calculate  the  temperature  of  the  exhaust  steam  when  the 
temperature  of  the  hot  well  is  108°  F. 

53.  An  engine  indicated  74  H.P.  and  the  heat  entering  the 
engine  per  minute  to  produce  this  power  was  24,300  B.T.U's. 
Calculate   (a)   the  heat  equivalent  of  the  I.H.P.,    (6)   the  heat 
admitted  to  the  engine  per  H.P.,  (c)  the  ratio  of  the  heat  equiv- 
alent of  the  I.H.P.  to  the  total  heat  admitted  to  the  engine.    How 
do  you  account  for  the  difference  between  the  heat  admitted  and 
the  heat  equivalent  of  the  I.H.P.? 

54.  A  steam-generating  plant  uses  2|  Ibs.  of  coal  per  I.H.P. 
per  hour.    If  the  heat  value  of  each  pound  of  coal  is  13,500  B.T.U's., 
what  is  the  ratio  of  the  heat  utilized  as  work  on  the  pistons  to  the 
heat  energy  of  the  fuel  producing  that  work?    Why  are  the  two 
quantities  not  equal? 

55.  The  temperature  of  the  injection  is  50°  and  of  the  dis- 
charge 102°  F.     Calculate  the  temperature  of  the  discharge  if  the 
temperature  of  the  injection  is  increased  to  60°  F.,  and  if  the 
weight  of  injection  is  increased  by  15  per  cent. 

NOTE.    Weight  of  injection  X  rise  in  temperature  =  constant. 

56.  A  boiler  evaporates  28,930  Ibs.   of  feed  water  from  a 
temperature  of  127°  into  steam  at  65  Ibs.  pressure  during  a  run 
of  10  hours.    What  H.P.  is  developed  by  the  boiler  if  rating  is 
based  upon  the  same  assumed  efficiencies  as  in  Problems  45  and  46? 


174  HEAT 

57.    A  compound  engine  and  dynamo,  direct  coupled,  gave 
the  following  results: 

I.H.P 15          23          37        48  62 

Output  (Kw.) .'..       5.4        8.8      16        22.5        31 

Total  steam  per  hr.  (Ibs.)..   435        580        822     1025         1290 

Plot  the  above  output  and  steam  used  to  a  base  of  I.H.P.  and 
add  curves  showing: 

.  Electrical  H.P. 

fa)  Mechanical  efficiency  of  combined  plant  =  - — .  TT  _ 

Indicated  H.P. 

(6)  Steam  used  per  I.H.P.  per  hour. 

(c)   Steam  used  per  Kw.  hour.  , 

.  58.  Find  the  fuel  cost  of  generating  electricity  per  Kw.  hr., 
from  the  above  curves,  if  the  average  output  be  25  Kw.,  the 
boiler  using  coal  at  $4.25  per  ton  and  evaporating  6|  Ibs.  of 
water  per  pound  of  coal. 

59.  How  many  pounds  of  water  could  be  evaporated  from  and 
at  212°  by  a  boiler  and  furnace  of  70  per  cent  efficiency  by  the 
coal  of  sample  14,  Table  IV? 

60.  How  many  pounds  of  water  could  be  evaporated  from  a 
feed-water  temperature  of  80°  F.  to  steam  at  120  Ibs.  gauge? 

61.  How  many  pounds  of  feed  water  could  be  heated  in  an 
open  feed-water  heater  from  60°  F.  to  200°  F.  by  a  pound  of  exhaust 
steam  of  a  quality  of  .850  at  atmospheric  pressure? 

62.  How  many  pounds  of  exhaust  steam  would  be  required 
to  heat  a  ton  of  feed  water  in  an  open  heater  from  70°  to  180°  F. 
if  895  quality  of  steam  at  16  Ibs.  was  used? 

63.  How  many  pounds  of  water  per  pound  of  combustible  will 
be  evaporated  in  Prob.  59? 

64.  A  boiler  plant  evaporates  6  Ibs.  of  water  per  pound  of  coal 
without  an  economizer.     The  steam  pressure  is  150  Ibs.;  feed  tem- 
perature, 120°.     By  adding  an  economizer  the  feed  temperature 
is  increased  to  230°.     If  the  same  quantity  of  heat  is  delivered 
to  the  boiler  when  the  economizer  is  used,  what  is  the  increase 
in  the  plant  efficiency? 

65.  If  the  coal  used  in  the  previous  problem  contained  13,600 
B.T.U.,  what  was  the  percentage  efficiency  both  with  and  with- 
out the  economizer? 

66.  An  engine  uses  24  Ibs.  of  steam  per  I.H.P.  per  hour.     Feed 
temperature,  120°;  steam  pressure,  135  Ibs.    The  boiler  evaporates 
8.8  Ibs.  of  water  per  pound  of  coal.    How  many  pounds  of  coal 
are  required  per  I.H.P.  per  hour? 


VI.     FUNCTIONS  OF  A  STEAM  POWER  PLANT    175 

67.  A  boiler  evaporates  8.6  Ibs.  of  water  per  pound  of  coal. 
Steam  pressure,  125  Ibs.;  feed  temperature,  150°.    What  weight 
of  water  per  Ib.  of  coal  will  it  evaporate  with  a  steam  pressure  of 
5  Ibs.  and  a  feed  temperature  of  180°? 

68.  A  boiler  evaporates  8000   Ibs.  of  water  per  ton  of  coal. 
Steam  pressure,   180  Ibs.;    feed  temperature,  50°.     What  will  it 
evaporate  if  the  steam  pressure  is  200  Ibs.  and  the  feed  tem- 
perature is  150°? 

69.  A  coal  contains  C,  78  per  cent;  H,  6  per  cent;  0,  3  per  cent. 
Efficiency  of  the  boiler  and  grate,  70  per  cent;   feed  temperature, 
180°;   steam  pressure,  150  Ibs.  absolute.     Steam  contains  2.2  per 
cent  moisture.     In  the  previous  problem  what  is  the  equivalent 
evaporation?     What  is  the  actual  evaporation  per  pound  of  coal? 
What  is  the  equivalent  evaporation  from  and  at  212°  per  pound 
of  coal? 

70.  A  boiler  is  reported  to  evaporate  12.5  Ibs.  of  water  per 
pound  of  coal.     Coal  contains  13,400  B.T.U.  and  uses  20  Ibs.  of 
air  per  pound  to  burn  it.    Temperature  of  the  boiler  room,  70°. 
Compute  the  percentage  efficiency  of  this  plant. 


176  HEAT 


SUMMARY,   CHAPTER  VI 

A  SIMPLE  STEAM-POWER  PLANT  contains  only 
three  members:  furnace,  boiler,  and  engine.  There  are 
three  currents  which  must  be  traced  through  the  plant : 
the  air  and  flue  gas  circuit,  the  water  circulation,  and  the 
energy  stream.  Large  steam-power  plants  introduce 
other  members  when  by  so  doing  a  reduction  of  cost 
efficiency  will  result.  Such  members  are  introduced  to 
reduce  the  energy  losses. 

A  STEAM  BOILER  takes  a  small  volume  of  water 
and  by  heating  it  up  delivers  it  as  steam  at  the  same 
pressure  as  taken  in,  but  with  a  greatly  increased  volume. 

THE  TRUE  EFFICIENCY  of  a  Steam  Boiler  is  not 
often  computed.  Results  which  are  labeled  "  Boiler 
Efficiency  "  are  usually  the  joint  efficiency  of  the  boiler 
and  furnace.  Efficiency  of  the  boiler  unit  is  expressed 
in  a  variety  of  ways. 

Factor  of  Evaporation  = 

Total  heat  of  steam— Total  heat  hi  feed  water 
970  ,  ' 

Water  Rate = pounds  of  steam  and  water  per  I.H.P.  hour. 

THE  ECONOMIZER  warms  the  feed  water  and  derives 
its  heat  from  the  hot  flue  gases  as  they  leave  the  boiler 
on  their  way  to  the  chimney. 

THE  FEED-WATER  HEATER  warms  the  feed 
water  and  derives  its  heat  from  the  hot  steam  exhausted  by 
either  the  main  engine  or  the  auxiliaries  or  both. 


VI.      FUNCTIONS  OF  A  STEAM  POWER  PLANT     177 

THE  BAROMETRIC  CONDENSER  reduces  the  back 
pressure  on  the  engine  by  liquefying  the  steam 
through  contact  with  a  steady  stream  of  cool  water. 

THE  SURFACE  CONDENSER  accomplishes  the 
same  result  without  mixing  the  steam  with  the 
circulating  water. 

THE  STEAM  ENGINE  moves  because  of  the  differ- 
ence of  pressure  upon  the  two  sides  of  the  piston  head. 

M.E.P.  for  a  stroke  is  the  average  difference  in  pressure 
on  the  two  sides  of  a  piston  during  that  whole  stroke. 

At  the  same  pressures,  the  distance  the  piston 
moves  depends  upon  the  volume  of  steam  supplied. 

The  WORK  Done  per  Stroke  =  Area  XM.E.P.X Length 
of  Stroke. 

There  are  usually  two  working  strokes  per  revolu- 
tion, and  for  each 

M.E.P.XAXNXL 
33000 

The  total  I.H.P.  is  the  sum  of  the  I.H.P.  for  each 
stroke. 

THE  RANKINE  CYCLE  states  the  theoretical  correct 
behavior  of  steam  in  an  ideal  engine.  The  formula  to 
express  the  efficiency  of  an  engine  working  on  this 
cycle  is 

Bff^lLi??. 

For  all-gas  cycle,  we  would  have  under  ideal  con- 
ditions 

Ti-T2 


CHAPTER  VII 
FUNCTION  OF  GAS  POWER  PLANTS 

60.  Comparative   Efficiency.      From    the    last    chapter, 
it  appears  that  in  the  very  best  modern  steam  plants  only 
about  a  sixth  of  the  heat  energy  in  the  fuel  is  converted  into 
mechanical  energy;    20  per  cent  is  usually  fixed   as    the 
practical  limit  of  efficiency  for  steam  power  plants.     The 
large  amount  of  heat  energy  of  vaporization  which  must 
be  lost  in  the  exhaust  of  the  steam  engine  limits  the  efficiency 
of  the  typical  arrangement  shown  in  Figs.  38  and  39.     Higher 
efficiencies  have  been  sought,  therefore,  in  a  different  type 
of  engine. 

The  perfection  of  the  explosion  type  of  engine  has 
progressed  to  a  point  where  it  is  successfully  competing 
with  the  steam  engine  in  many  industries.  The  gas  engine 
has  been  particularly  successful  in  small  installations  and  in 
motor  vehicle  work.  It  has  shown  greater  efficiency  from 
an  energy  efficiency  standpoint  in  practically  every  field. 
However,  when  the  cost  of  fuel,  labor,  maintenance,  deprecia- 
tion, etc.,  is  considered,  the  "  Cost  Efficiency "  is  not  so 
certainly  in  favor  of  the  explosion  type  of  engine. 

By  "  Cost  Efficiency "  is  meant  the  H.P.  hours  per 
dollar  expended  for  fuel,  labor,  overhead  charges,  etc. 

61.  Fuel.     The    explosion   engine   is   always   a    "  gas " 
engine,  though  gas  power  plants  are  run  with  every  type 
ofc  oal,  all  grades  of  oil,  and  all  of  the  various  kinds  of  gas 
fuels.     In  the  case   of  coals  and  oil  there   must  be  some 
means  provided  to  change  the  fuel  to  a  gas  and  to  mix  it 
with  air  (containing  the  oxygen  to  support  the  combustion) 

178 


VII.      FUNCTION  OF  GAS  POWER  PLANTS        179 

before  attempting  to  explode  the  mixture  in  the  cylinder  of 
the  engine. 

The  carbureter  (for  light  oils)  or  the  vaporizer  (for  heavy 
oils)  is  used  to  evaporate  the  liquid  and  to  mix  the  gas  with 
the  proper  proportion  of  air  before  admitting  the  fuel  to 
the  cylinder. 

The  Diesel,  the  Mietz  &  Weiss,  and  all  of  the  other 
so-called  oil  engines  which  inject  liquid  fuel  into  the  cylinder, 
depend  upon  some  means  of  spraying  the  liquid  and  some 
method  of  maintaining  a  temperature  in  the  cylinder  which 
will  vaporize  the  fuel  and  will  cause  combustion  at  the 
proper  time.  (See  discussion,  p.  29.) 

62.  Firing.  The  explosion  must- occur  at  a  very  definite 
position  of  the  piston  to  give  the  best  results  and  an  ignition 
system  adapted  to  the  type  of  engine  used  and  to  the  fuel 
is  necessary. 

Most  .engines  are  fired  by  an  electric  spark.  The 
various  so-called  electrical  ignition  systems  all  fall  under 
the  two  general  classifications:  JUMP-SPARK  (or  high-ten- 
sion system)  and  M AKE-AND-BREAK  (or  low-tension  system) . 
HOT  BALL  and  HOT  TUBE  ignition  systems  are  also  used. 
The  Mietz  <fe  Weiss  engine  described  on  p.  181  illustrates 
this  latter  type  of  system. 

The  jump-spark  systems  all  use  a  spark  plug  in  the 
cylinder.  The  plug  has  two  pointed  terminals  inside  the 
cylinder  connected  to  a  source  of  potential  and  a  high  volt- 
age causes  a  spark  to  jump  from  one  terminal  to  the 
other  and  thus  ignites  the  gas. 

The  make-and-break  systems  all  require  a  finger  inside 
the  cylinder.  This  finger  moves  forward  and  makes  con- 
tact with  the  wall  of  the  cylinder.  Then,  at  the  exact  instant 
when  an  explosion  is  desired,  the  finger  is  made  to  move 
away  quickly.  This  breaks  the  mechanical  contact  of  the 
surfaces.  The  effect  is  to  break  the  electrical  circuit,  and 
spin  out  an  arc.  This  finger  is  usually  operated  from  a 
cam  on  the  main  shaft. 


ISO  HEAT 

These  systems  differ  only  in  the  details  of  the  arrange- 
ment of  the  various  essential  parts.  The  electrical  theory 
upon  which  each  depends  will  be  found  in  electrical  text 
books. 

63.  Cycles.  The  term  cycle,  when  applied  to  gas  engines, 
does  not  differ  essentially  from  its  meaning  as  stated  in 
the  previous  chapter.  It  should  simply  be  remembered 
that  the  exploded  gases  are  not  used  over  again  in  the  cylin- 
der as  in  the  case  of  steam,  but  are  exhausted  into  the  air. 

The  time  of  mixing  the  fuel  with  the  gases  which  are  to 
supply  the  oxygen  differs  in  the  various  types  of  engines, 
and  these  differences  have  resulted  in  such  terms  as  "  Otto 
Cycle,"  "  Diesel  Cycle/',  etc. 

The  chief  basis  of  classification  of  engines  as  to  cycles 
depends  upon  the  number  of  strokes  of  the  engine  per 
explosion.  The  two-cycle  engine  gives  an  explosion  every 
revolution  of  the  crank  shaft,  or  one  explosion  for  every 
two  strokes.  The  four-cycle  engines  give  an  explosion 
during  each  alternate  revolution  of  the  crank  shaft,  or  one 
explosion  for  every  four  strokes. 

The  characteristic  of  design  which  has  tended  to  make  the  two- 
cycle  engine  so  simple  is  illustrated  by  Fig.  49.  This  feature  is  the 
complete  absence  of  valves  in  the  cylinder.  By  using  an  enclosed 
crank  case  a  mixture  of  air  and  fuel  may  be  sucked  into  the  crank 
case  during  the  "  idle  stroke  "  by  the  partial  vacuum  produced  by  the 
piston  moving  out  away  from  the  crank  shaft.  The  opening  marked 
"  suction  port  "  in  the  figure  may  be  connected  to  a  carbureter  when 
gasoline  is  used.  When  the  cylinder  moves  back  on  the  "  working 
stroke  "  the  charge  in  the  crank  shaft  is  compressed.  When  the  stroke 
has  progressed  to  a  point  where  the  air  port  is  uncovered  the  charge 
is  by-passed  through  134  into  the  cylinder.  On  the  piston  head  is  a 
projection  which  deflects  the  air  upward  into  the  cylinder  and  away 
from  the  exhaust  port.  As  the  piston  moves  back  on  its  "  return 
stroke  "  the  charge  is  compressed  and  finally  exploded  as  the  engine 
passes  dead  center.  On  the  "  forward  stroke  "  the  exhaust  port  is 
uncovered  before  the  admission  air  port  is  uncovered.  The  pressure 
in  the  cylinder  falls  to  atmospheric  before  admission  takes  place  and 
therefore  the  compressed  charge  in  the  crank  case  comes  in  with  a  rush 


VII.     FUNCTION  OF  GAS  POWER  PLANTS         181 

and  sweeps  out  through  the  exhaust  port  the  burned  gases  produced 
by  the  explosion.  The  cycle  of  events  is  complete  and  is  repeated 
indefinitely. 

The  engine  shown  has  special  features  of  construction  to  permit 
liquid  fuel  to  be  used.  Fuel  is  injected  just  before  the  engine  reaches 
dead  center  by  the  pump  40,  operated  from  the  crank  shaft.  Only 
air  therefore  is  compressed  in  the  crank  case.  64  is  a  hot  ball  in  an 
enclosed  insulated  chamber.  To  start  the  engine  this  is  heated,  with 


FIG.  49.— Mietz  &  Weiss  Two-Cycle  Engine. 


a  torch,  94,  to  a  red  heat.  When  the  fuel  is  injected  by  the  pump  40 
it  impinges  upon  the  spoon-like  projection  of  64,  which  is  red  hot. 
It  is  at  once  vaporized  by  this  heat,  and  mixed  with  the  air.  It  is 
exploded  by  the  heat  of  compression.  The  fuel  is  pumped  at  the 
proper  time  in  the  stroke  by  the  governing  device  27,  hitting  the 
piston  rod  extension  of  pump  43. 

The  four-cycle  engine  is  more  complicated  and  always  has  valves 
which  are  operated  usually  from  a  counter  shaft.  This  is  frequently 
called  the  cam  shaft  or  half-speed  shaft.  Poppet  valves  are  almost 


182 


HEAT 


always  used.  In  Fig.  50  an  Otto  four-cycle  engine  is  shown.  Fig. 
51  shows  a  section  through  the  cylinder  head  and  valve  mechanism. 
The  charge  enters  the  cylinder  through  the  poppet  valve  A.  The 
valve  stem  C  is  operated  from  the  shaft  which  carries  the  inlet  cam  H 
through  G,  E,  and  D.  M,  on  the  same  shaft,  operates  the  exhaust 
valve  /  through  the  stem  A'  and  the  arm  L. 


FIG.  50. — Otto  Four-cycle  Engine. 

S  is  a  make-and-break  igniter  which  is  energized  from  the  oscillating 
magneto.  The  mechanism  by  which  this  is  operated  is  not  shown  in 
the  cut. 

64.  Fuel  Circulation  in  a  Producer  Gas  Power  Plant. 

A  producer  gas  power  plant  may  be  divided  into  two  parts 


VII.      FUNCTION  OF  GAS   POWER  PLANTS        183 

for  purposes  of  discussion.  First,  a  gas-producing,  cleansing 
and  storage  system,  and  second,  an  explosion  engine  or 
motor  as  it  is  often  called.  The  gas-producing  part  of  the 


FIG.  51. — Sectional  View  of  Valve  Mechanism  of  the  Otto  Engine. 

plant  may  equally  well  provide  producer  gas  to  run  a  furnace 
or  for  any  purpose  for  which  a  fuel  gas  may  be  used.  The 
engine  may  be  similar  to  the  Otto  engine  just  described  or 
any  other  designed  to  use  a  gas  fuel  of  this  general  character. 


184 


HEAT 


Because  of  limited  space,  only  one  gas  power  plant 
can  receive  detailed  attention  in  this  book.  A  suction  gas 
producer  plant  has  been  selected  for  study  and  the  arrange- 
ment of  its  members  is  shown  in  Fig.  53.  Fig.  54  shows 
the  energy  circulation  through  this  plant. 

The  drawings  for  Figs.  53,  54,  63  and  64  were  made 
by  students  of  the  Applied  Chemistry  Class  of  1913  as 
optional  problems.  Figs.  53  and  54  are  for  a  plant  similar 


FIG.  52. — Suction  Producer  Plant  with  Otto  Engine. 

to    that    shown   in    Fig.    52   except    that    they    have  two 
additional  features,  as  will  appear  presently. 

Producer  gas  plants  may  be  designed  to  burn  any  type  of  coal,  and 
it  is  usual  to  construct  them  to  burn  the  coal  which  is  cheapest  in  the 
town  where  they  are  to  be  used.  They  are  particularly  efficient  from 
a  "  Cost  Efficiency  "  standpoint  when  using  certain  low-grade  coals. 

The  chemical  action  that  takes  place  in  the  various  types  of  gas 
producer  is  essentially  the  same.  In  the  gas  producer,  or  generator, 
shown,  coal  is  fed  in  at  the  top,  and  the  hot  gases  coming  through  the 
fuel  bed  heat  up  the  fresh  coal.  Because  of  this  heating,  the  volatile 
matter  is  first  driven  off,  then  carried  through  the  various  members 
of  the  plant  and  finally  delivered  to  the  engine  cylinder.  Then  as  the 
coal  settles  it  becomes  white  hot,  and  at  that  temperature  it  is  very 
eager  to  unite  with  oxygen.  This  affinity  for  oxygen  is  so  strong 
that  any  gaseous  carbon  atom  which  has  taken  on  two  atoms  of  oxygen 
and  is  rising  through  the  fuel  bed  as  CO2  is  readily  reduced,  i.e.,  made 
to  give  up  one  O  by  a  second  carbon  atom,  and  two  molecules  of  CO 


VII.     FUNCTION  OF  GAS  POWER  PLANTS        185 

pass  on  to  the  engine.  As  the  coal  drops  down  still  further,  the  incom- 
ing stream  of  air  is  richer  in  oxygen  and  the  remaining  coal  burns  to 
CO2  and  supplies  the  heat  to  keep  the  process  going. 

With  the  air,  a  small  amount  of  steam  is  often  supplied,  partly 
to  prevent  clinkers  forming  and  partly  to  supply  the  incandescent 
coal  with  another  molecule  containing  oxygen  which  the  carbon  can 
take  over.  The  water,  H2O,  is  broken  down  into  hydrogen,  H,  which 
is  very  combustible,  and  oxygen,  O,  which  at  once  unites  with  the 
carbon  in  the  coal  to  form  CO.  For  each  pound  of  H2O  broken  down 
1873  B.T.U.  must  be  taken  from  the  fire.  When  the  H  from  this  H2O  is 
burned  in  the  cylinder  this  same  amount  of  energy  is  returned  as  heat. 

The  principal  differences  between  the  various  types  of  generators 
used  in  producer  gas  plants  occur  in  the  percentages  of  H2O  (steam) 
used  and  the  treatment  of  the  volatile  matter. 

The  gases,  as  they  rise  from  the  top  of  the  coal,  in  a  producer  gas 
plant,  contain  elements  and  compounds  from  the  coal  such  as  CO, 
H,  O,  and  N  (nitrogen).  The  nitrogen  was  in  the  air  and  has  not 
been  changed  in  chemical  composition.  Some  idea  of  the  relative 
per  cent  of  each  of  these  gases  present  may  be  gained  by  referring  to 
Table  V,  Nos.  1,  8  and  9. 

These  gases  are  very  hot.  They  are  first  shown  to  pass  through  an 
economizer  in  which  they  give  up  some  of  their  heat  to  the  air  which 
is  being  supplied  to  the  producer.  Next  they  pass 'into  a  boiler  which 
supplies  the  steam  which  is  fed  to  the  producer. 

From  the  boiler,  they  pass  into  the  scrubber,  where  all  dust,  ammo- 
nia and  tarry  volatile  substances  are  deposited.  As  they  pass  upward 
through  the  wet  coke  which  nearly  fills  the  scrubber,  they  are  cooled 
to  the  water  temperature,  which  causes  the  less  volatile  products  to 
change  to  a  liquid  which  is  deposited  on  the  coke. 

A  storage  tank  receives  the  gases  coming  from  the  scrubber.  This 
tank  is  merely  large  enough  to  prevent  a  sudden  rush  of  gas  through 
the  apparatus  when  the  engine  is  sucking  a  charge,  and  a  later  halting 
of  the  flow  after  the  admission  valve  closes.  It  equalizes  the  pressure 
through  the  scrubber  and  producer  and  makes  their  action  more  cer- 
tain and  uniform. 

Whether  the  gas  which  supplies  energy  to  an  engine 
is  supplied  by  a  gas  producer,  from  the  public  gas  plant, 
from  a  natural  gas  well,  or  from  a  vaporizer,  it  must  be 
mixed  with  a  proper  amount  of  air  (to  obtain  oxygen)  before 
it  will  burn  in  the  cylinder.  The  air  and  gas  are  drawn 
into  the  engine  through  suitable  mixing  valves  and  there 


186 


HEAT 


VII.     FUNCTION  OF  GAS  POWER  PLANTS        187 


188  HEAT 

exploded  by  an  electric  spark  at  the  proper  time.  The 
high  pressure  produced  by  the  explosion  moves  the  piston 
out  and  useful  work  is  done  by  the  expanding  gases.  Thus 
it  follows  that  the  principle  of  operation  of  the  explosion 
engine  is  very  similar  to  that  in  a  steam  engine.  The 
working  medium  is  under  high  pressure  during  the  early 
part  of  the  working  stroke  and  expands  nearly  adiabatically 
during  the  remainder  of  the  stroke.  The  I.H.P.  of  a  gas 
engine  may  be  obtained  in  exactly  the  same  way  as  I.H.P. 
of  a  steam  engine  (see  p.  151).  The  mean  effective  pressure 
is  computed  from  an  indicator  diagram  obtained  by  using 
a  Watts  indicator  in  exactly  the  same  way  as  with  the 
steam  engine. 

These  gases  are  very  hot  and  tend  to  heat  the  walls 
of  the  cylinder  and  the  piston.  The  temperature  of  the 
gases  at  the  explosion  is  high  enough  to  melt  the  iron  in 
the  cylinder.  To  have  satisfactory  lubrication  the  metal 
parts  must  be  kept  cool,  and  for  this  purpose  water  is  usually 
circulated  through  a  jacket  placed  about  the  cylinder. 
In  large  engines  the  cylinder  head  and  the  piston  are  water 
cooled  as  well.  This  water  carries  away  much  of  the  heat 
energy  of  the  fuel,  and  inevitably  decreases  the  efficiency 
of  the  engine. 

When  the  exhaust  port  opens,  the  pressure  is  still  above 
that  of  the  atmosphere  and  when  the  gases  leave  the  cylin- 
der they  are  still  very  hot.  Consequently,  much  of  the 
heat  energy  in  the  fuel  is  lost  in  the  exhaust. 

65.  Energy  Circulation.  In  the  energy  diagram,  Fig. 
54,  the  flow  of  heat  energy  through  this  system  is  shown. 
In  a  complete  energy  cycle  there  are,  at  the  start,  three 
sources  of  energy.  The  primary  source  is  .7  Ib.  of  coal, 
which  contains  7850  B.T.U.  of  heat  energy.  Returning 
from  a  previous  cycle,  540  B.T.U.  are  brought  back  in 
"sensible  "  heat  by  the  preheated  air  supply.  In  the  same 
way  400  B.T.U.  more  than  were  in  the  water  at  atmospheric 
temperature  are  returned  in  the  live  steam  supply. 


VII.     FUNCTION  OF  GAS  POWER  PLANTS        189 

The  figure  also  shows  the  losses.  In  the  generator 
they  are  due  to  radiation  and  ash.  The  losses  in  the  air 
heaters  are  due  to  radiation.  540  B.T.U.  are  shown  to 
be  credited  to  the  interchanger.  400  B.T.U.  are  credited 
to  the  boiler,  because  of  the  energy  returned  in  the  live 
steam  to  the  generator.  260  B.T.U.  are  lost  in  the  boiler 
due  to  radiation,  leakage,  steam  used  for  other  service 
purposes,  etc.  Piping  is  also  charged  with  radiation  losses. 
The  scrubber  loses  500  B.T.U.,  some  of  which  is  due  to 
radiation,  but  a  larger  part  is  due  to  the  cooling  effect 
of  the  water.  As  the  gases  rise  from  the  coal  in  the 
generator  they  have  a  temperature  which  probably  exceeds 
1500°  F.  While  the  gases  are  in  contact  with  the  water 
they  are  cooled  to  the  temperature  of  the  water  and  con- 
sequently give  up  heat.  In  the  engine  there  is  a  friction 
leakage,  and  fuel  waste  of  375  B.T.U.  To  cool  the  cylinder, 
water  is  circulated  in  a  jacket  and  the  water  takes  away  2804 
B.T.U.  In  the  exhaust  1750  B.T.U.  are  lost  in  the  sensible 
heat  of  the  gases.  1840  B.T.U.  appear  as  B.H.P.  hour 
useful  work. 

The  scientific  way  to  express  the  efficiency  of  a  pro- 
ducer gas  power  plant  is  to  give  the  per  cent  of  the  avail- 
able energy  in  the  coal  that  is  delivered  by  the  engine  in  the 
form  of  useful  work.  The  efficiency  of  the  gas-producing 
equipment  is  the  B.T.U.  fuel  value  in  the  gas  as  it  leaves 
the  scrubber  divided  by  the  total  B.T.U.  in  the  coal  from 
which  the  gas  was  produced.  This  is  usually  given  in  per 
cent.  The  efficiency  of  the  engine  is  the  useful  energjr 
delivered,  divided  by  the  energy  in  the  gas  supplied  to  the 
engine  as  fuel.  This  ratio  is  usually  given  in  per  cent. 

Problem  1.  What  was  the  efficiency  of  the  engine  in 
Fig.  53? 

Problem  2.  What  was  the  weight  of  coal  required  per  H.P. 
hour  by  the  plant  of  Fig.  53? 

Problem  3.  What  was  the  over-all  plant  efficiency  of 
Fig,  53? 


190  HEAT 

Problem  4.  What  was  the  efficiency  of  the  gas  generating 
equipment  in  Fig.  53? 

Problem  5.  What  per  cent  of  the  energy  delivered  to  the 
engine  was  lost  in  the  exhaust? 

Problem  6.  What  per  cent  of  the  energy  delivered  to  the 
engine  was  taken  away  by  the  circulating  water? 

Problem  7.  If  6  Ibs.  of  air  by  weight  were  used  per  pound  of 
coal  what  was  the  amount  of  preheating? 

Problem  8.  If  the  atmospheric  temperature  and  feed-water 
temperature  are  the  same,  and  the  pressure  of  the  steam  5.3 
Ibs.  gauge,  what  weight  of  steam  was  added  for  each  .7  Ib.  of 
coal? 

Problem  9.  If  there  was  an  equal  weight  of  air  mixed  with 
the  gas  before  explosion,  bearing  in  mind  the  conditions  men- 
tioned in  Probs.  7  and  8,  compute  the  temperature  of  the  exhaust 
gases.  (Assume  the  specific  heat  of  the  gases  to  be  the  same 
as  air.) 

Problem  10.  What  must  have  been  the  temperature  imme- 
diately after  the  explosion  in  the  cylinder,  assuming  all  of  the 
conditions  to  hold  as  in  Probs.  7,  8,  and  9.  The  engine  has  25 
per  cent  clearance  and  combustion  is  completed  while  engine  is 
still  on  dead  center. 

NOTE.  It  is  not  true  that  the  specific  heat  is  constant  under 
all  the  conditions  mentioned,  but  for  the  purposes  of  these  prob- 
lems it  will  do  to  use  the  value  given  in  Table  VI  for  air. 

Problem  11.  There  is  a  theory  that  the  ideal  efficiency  of  a 
heat  engine  is  expressed  by  the  following  ratio  where  the  tem- 
peratures are  absolute,  and  T\  equals  the  temperature  of  charge 
after  explosion  and  Tz  equals  the  temperature  of  exhaust. 


How  nearly  does  it  agree  with  your  computed  results  in  the  pre- 
vious problems? 

Problem  12.  Draw  an  energy  diagram  showing  1  H.P.  hour 
of  useful  work  output  for  a  liquid  fuel  used  in  an  explosion 
engine.  The  efficiency  of  the  engine  is  28  per  cent.  Loss  in 
cooling  water  and  radiation  is  40  per  cent.  Two  per  cent  of 
energy  is  lost  in  vaporizing  the  liquid  and  in  leakage,  30  per 
cent  is  lost  in  the  exhaust.  There  are  19,000  B.T.U.  per  pound 
in  the  fuel. 


VII.     FUNCTION  OF  GAS  POWER  PLANTS        191 

66.  Explosive  Mixtures.  The  relative  weights  of  fuel 
and  air  which  must  be  used  to  produce  complete  combus- 
tion may  be  computed  from  the  information  given  in  Chap- 
ter II.  It  may  be  possible  to  produce  an  explosion  if  the 
mixture  deviates  from  this  theoretical  amount.  How  great 
a  deviation  from  the  ideal  proportion  is  allowable  is  dependent 
upon  the  construction  of  the  engine  and  the  type  of  fuel. 
Allen  and  Bursley  state  that  the  per  cent  by  volume  of  fuel 
which  when  mixed  with  air  will  explode,  varies  from  16  to 
74  per  cent  for  CO,  from  8  to  17  per  cent  for  illuminating  gas, 
and  from  2|  to  5  per  cent  for  gasoline.  The  most  econom- 
ical results  will  be  obtained  with  mixtures  containing  -less 
than  the  theoretical  amount  of  fuel. 

To  operate  any  explosion  engine  below  full  load,  some 
method  of  governing  is  necessary.  Stationary  engines  are 
often  governed  by  the  "  hit  or  miss  "  method.  With  this 
method  fuel  is  admitted  to  the  cylinder  only  at  such  times 
as  the  speed  is  below  a  certain  maximum.  This  method 
is  economical,  but  results  in  a  very  irregular  speed.  Gov- 
erning is  more  often  produced  by  throttling.  By  this 
means  the  amount  of  fuel  is  reduced  and  the  engine  is 
"  starved."  Economical  results  follow  at  light  loads. 
When  the  throttle  is  operated  by  hand,  as  in  the  gasoline 
automobile  engine,  the  range  of  speeds  obtainable  is  not 
low  enough  at  no  load.  Further  control  is  obtained  by 
adjusting  the  time  of  a  spark.  Those  devices  are  most 
economical  which  control  the  gas  supply  and  never  allow 
the  mixture  to  exceed  the  theoretical  per  cent  of  fuel. 
At  the  same  time  they  should  not  reduce  the  fuel  per  cent 
far  below  the  theoretical  value. 

The  theoretical  per  cent  of  air  required  for  complete 
combustion  may  be  computed  in  a  much  simpler  manner 
than  in  Chapter  II  when  the  analysis  is  by  volume.  The 
computation  for  a  sample  of  illuminating  gas  follows: 


192 


HEAT 


Gas  Contained. 

Per  Cent  by 
Volume. 

Volume  of  Oxygen 
in  Per  Cent 
of  Total  Volume 
of  Coal  Gas. 

Hydrogen  (H2)                

48 

24 

Marsh  gas  (CH4)  

39.5 

79 

Illuminants  (CnH2n)  

3.8 

17.1 

Carbon  monoxide  (CO)  
Nitrogen   .        

7.5 
0  5 

3.7 

Oxygen 

0  7 

0  7 

100 

123.1 

The  values  of  the  second  column  are  obtained  as  follows : 
It  is  known  that  two  volumes  of  hydrogen  unite  with  one  of 
oxygen  to  form  water  and  the  accepted  chemical  formula 
is  2(H2)+02  =  2(H20).  Therefore  half  as  much  oxygen 
by  volume  as  hydrogen  is  required.  Similarly  one  volume 
of  CH4  unites  with  two  volumes  of  oxygen  according  to 
the  formula: 

CH4+2(O2)  =  C02+2(H20). 

Therefore  the  volume  of  oxygen  given  in  the  table  is  twice 
as  great  as  that  of  the  CH4.  Likewise  if  n  equals  3  the 
illuminants  would  then  be  exclusively  CsHe.  This  is 
assumed  and  the  reaction  would  then  be : 

2(C3H6)  +9(O2)  =  6(C02)  +6(H20). 

Thus  4  J  volumes  of  oxygen  would  be  required  for  each  volume 
of  CsHe.  Finally  two  volumes  of  CO  unite  with  one  volume 
of  O2  to  make  C02  according  to  the  formula : 

2(CO)+02  =  2(C02). 

Therefore  only  half  as  much  oxygen  as  carbon  monoxide 
is  required. 


VII.     FUNCTION  OF  GAS  POWER  PLANTS        193 

By  adding  algebraically  the  per  cents  of  oxygen  it  is 
found  that  for  100  parts  of  gas  123.1  parts  of  oxygen  would 
be  required.  Since  there  are  20.7  volumes  of  oxygen  in  100 
volumes  of  air,  to  obtain  1.23  volumes  of  oxygen  will 
require  that  5.95  volumes  of  air  be  injected  into  the  cylinder. 

The  combining  volumes  of  the  other  compounds  men- 
tioned in  Table  V  may  be  obtained  from  the  chemical 
formulas  which  show  how  they  combine  with  oxygen. 
These  formulas  follow; 

(C2H4)+3(02)  =  2(C02)+2(H20) 
2(H2S)+5(02)=2(S02)  +2(H20) 

2(C2H2)  +5(02)  =  4(C02)  +2(H20) 

In  all  of  the  above  computations  it  must  be  understood 
that  all  of  the  gases  are  at  the  same  standard  temperature. 
For  a  detailed  statement  covering  other  compounds,  and 
more  complicated  conditions,  the  student  is  referred  to 
works  on  chemistry. 

Problem  13.  What  would  be  the  theoretical  volume  of  air 
required  for  each  volume  of  gas  in  analysis  1,  Table  V? 

Problem  14.  How  much  air  would  be  required  to  burn  sample  2, 
Table  V? 

Problem  15.  If  an  engine  operated  with*  the  conditions  of 
combustion  as  in  Prob.  13,  and  if  25  per  cent  of  the  energy  in  the 
fuel  was  carried  from  the  engine  in  the  exhaust  gases,  what  was 
the  temperature  of  the  exhaust  as  it  passed  into  the  atmosphere. 
(Assume  atmospheric  pressure,  a  specific  heat  the  same  as  for  air, 
and  no  velocity  effect.) 

Problem  16.  What  per  cent  of  the  heat  energy  lost  in  the 
exhaust  was  carried  away  by  the  inert  nitrogen  in  Prob.  13? 

Problem  17.  What  per  cent  of  the  total  heat  energy  of  the 
fuel  was  carried  away  by  the  exhaust  in  Prob.  13? 

Problem  18.  If  in  Fig.  39,  12  Ibs.  of  air  were  required  per  pound 
of  coal,  what  was  the  stack  temperature?  What  per  cent  of  the 
energy  lost  was  due  to  the  heat  in  the  inert  nitrogen  as  it  passed 
up  the  stack? 


194  HEAT 

67.  Working  Medium.  In  texts  upon  heat  engines  the 
substances  used  in  the  cylinder  to  exert  a  pressure  against 
the  piston  are  called  the  working  medium. 

In  the  steam  power  plant  we  use  water  as  a  working 
medium  and  supply  energy  to  it  outside  the  cylinder  in  a 
boiler.  We  have  already  seen  the  low  efficiency  which 
must  follow  the  use  of  water  for  this  purpose. 

In-  the  gas  engine  we  always  use  as  our  working  medium 
the  products  of  combustion  of  our  fuel.  In  all  engines, 
so  far  used  commercially,  the  combustion  takes  place  in  the 
cylinder  itself.  From  the  preceding  problems  it  is  seen 
that  about  70  per  cent  of  this  working  medium  is  nitrogen, 
which  simply  serves  to  dilute  the  products  of  combustion 
of  the  fuel.  The  inevitable  losses  in  both  the  steam  plant 
and  the  gas  power  plant  from  handling  this  large  weight 
of  waste  material  are  very  large. 

The  theoretically  correct  solution  of  the  problem  of 
economically  utilizing  fuels  will  doubtless  be  obtained 
through  the  perfection  of  some  one  of  the  many  schemes  for 
burning  the  fuel  outside  the  engine  and  then  expanding  the 
gaseous  products  of  combustion  in  a  suitable  engine  or  tur- 
bine until  their  temperature  and  total  energy  do  not  greatly 
exceed  the  energy  in  the  gases  of  the  atmosphere.  Many 
such  experimental  plants  have  been  devised  and  patented, 
but  none  have  come  into  commercial  use.  Models  have 
shown  better  efficiency  than  any  commercial  plant  now  in 
use,  but  it  has  not  been  possible  to  find  materials  which, 
without  deterioration,  would  stand  the  temperatures  re- 
quired. 


VII.     FUNCTION  OF  GAS  POWER  PLANTS        195 


REVIEW  PROBLEMS,    CHAPTER   VII 

19.  A  gasoline  engine  uses  1.2  Ibs.  of  oil,  containing  18,200 
B.T.U.,  per  brake  horse-power  per  hour.     It  is  assumed  that  the 
losses  are  as  follows : 

2  per  cent  of  the  total  loss  is  friction; 

3  per  cent  is  unburned  fuel; 

40  per  cent  is  thrown  out  in  the  exhaust ; 
55  per  cent  is  carried  away  in  the  jacket  water. 
Draw  energy  diagram  for  this  engine. 

20.  What  is  the  heat  efficiency  of  this  engine? 

21.  What  is  the  oil  consumption  per  I.H.P.  of   the  engine  in 
Prob.  19? 

22.  If  this  is  a  single-cylinder  four-cycle  engine,  making  1200 
r.p.m.,  delivering   16  H.P.,  having  an  8-in.  stroke,  and  a  piston 
area  of  20  sq.ins.,  what  is  its  M.E.P.? 

23.  A  gas  engine  uses  20  cu.ft.  of  gas  per  horse-power  per  hour. 
Each  cubic  foot  of  gas  contains  550  B.T.U.    The  initial  temper- 
ature in  the  engine  is  2100°  F.,  and  the  final  temperature  is  850°  F. 
What  is  the  heat  efficiency? 

24.  What  is  the  "ideal  efficiency"  as  an  ideal  heat  engine  in 
Prob.  23? 

25.  An  engine  has  an  8-inch  stroke  and  24  sq.ins.  piston  area. 
It  is  two  cycle  and  running  at  300  r.p.m.     Its  M.E.P.  is  80  Ibs. 
It  exerts  a  force  of  21  Ibs.  at  a  radius  of  66  ins.     What  is  the  force 
of  energy  lost  in  friction?    Comment  on  the  probable  mechanical 
condition  of  this  engine. 

26.  A  gas-engine  cylinder  is  9  ins.  diameter,  its  stroke  16  ins., 
mean  pressure  75  Ibs.  per  square  inch,  revolutions  180,  explosions 
85,  diameter  of  flywheel  5  ft.,  friction  of  brake  band  160  Ibs.,  gas 
used  per  hour  250  cu.ft.  of  a  thermal  value  of  600  B.T.U.  per  cubic 
foot.    Find  the  I.H.P.,  B.H.P.,  thermal  efficiency,  and  mechan- 
ical efficiency. 

27.  The  cylinder  of  a  four-cycle  gas  engine  is  16  ins.  in  diameter, 
the  stroke  is  24  ins.     Clearance  is  20  per  cent.    Find: 

1.  (&i)  volume  in  cubic  feet  at  end  of  admission  stroke. 

2.  (02)  volume  in  cubic  feet  at  end  of  compression  stroke. 


196  HEAT 

28.  Charge  in  above  engine  is  taken  in  at  14.7  Ibs.  pressure 
and  at  60°  F.     Find: 

(1)  Weight  of  charge  if  1  cu.ft.  weighs  .0087  Ib.  at  14.7  Ibs. 

per  square  inch  and  32°  F. 

(2)  Weight  of  entire  mixture  in  cylinder  at  end  of  admis- 

sion stroke. 

29.  If  the  pressure  at  end  of  compression  stroke  is  181  Ibs.  per 
square  inch,  what  is  the  temperature? 

30.  If  the  charge  consists  of  1  part  gas  and  9  parts  air,  what 
is  the  temperature  at  end  of  explosion? 

NOTE.  Use  Heat  of  Combustion  as  600  B.T.U.'s  per  cubic  foot 
of  gas  at  end  of  admission.  Use  specific  heat  of  air  at  con- 
stant volume. 

31.  What  is  the  pressure  at  end  of  the  explosion? 

32.  Assuming  the  pressure  at  end  of  explosion  is  12.3  times  as 
great  as  at  end  of  expansion  stroke,  what  is  the  pressure  and  tem- 
perature at  end  of  expansion  stroke? 

33.  If  the  engine  makes  180  r.p.m.,  what  horse-power  does  it 
develop?    Assume  an  efficiency  of  30  per   cent, 


VII.     FUNCTION  OF  GAS  POWER  PLANTS        197 


SUMMARY,  CHAPTER  VII 

GAS  POWER  PLANTS  show  greater  thermal  efficiency 
than  steam  power  plants  and  frequently  better  cost 
efficiency.  For  small  plants  they  are  unquestion- 
ably superior  to  steam. 

FUEL  is  either  supplied  to  the  cylinder,  as  a  gas  or 
is  changed  to  a  gas  in  the  cylinder  before  combustion 
takes  place. 

FIRING  is  the  term  applied  to  the  igniting  of 
the  fuel.  It  is  accomplished  in  those  engines  in  which 
electrical  ignition  is  employed  by  either  a  make-and- 
break  system  or  a  jump  spark  system. 

TWO-CYCLE  and  four-cycle  usually  refer  to  the 
number  of  strokes  per  explosion.  Special  cycle  names 
are  used  to  describe  the  method  of  introduction  and 
the  condition  of  the  fuel  when  introduced. 

GAS  PRODUCERS  are  commonly  used  to  supply 
fuel  in  the  gaseous  form,  to  an  explosion  engine  from 
an  original  supply  of  coal.  A  Producer-Gas  Power 
Plant  is  any  combination  of  a  gas  producer  and  a  gas 
engine. 

EXPLOSIVE  MIXTURES  are  usually  quick  burn- 
ing, well-proportioned,  intimate  mixtures  of  a  gaseous 
fuel  and  oxygen. 

WORKING  MEDIUM  is  an  expression  used  to 
refer  to  the  heat  vehicle  in  an  engine. 


CHAPTER  VIII 
EXPANSION  OF  GASES  (Continued} 

THE  most  difficult  theory  for  the  student  to  understand 
and  apply  is  that  which  explains  the  expansion  of  gases 
in  cylinders  of  engines,  compressors,  etc.  The  complex 
conditions  which  exist,  however,  when  analyzed  step  by 
step,  become  clear. 

/  68.  Specific  Heat  of  a  Gas.  The  first  point  to  be 
noted  is  thafca  gas  has  two  specific  heats. 

/"  The  specific  heat  at  constant  volume  (C9)  of  a  gas  is 
the  heat  energy  required  to  raise  the  temperature  of  a  unit 
mass  of  gas  one  degree  without  a  change  in  volume. 

The  numerical  value  of  the  specific  heat  at  constant  volume  is  prac- 
tically the  same  for  air,  oxygen,  nitrogen,  CO,  CO2,  and  mixtures 
found  in  gas  engine  cylinders  at  ordinary  temperatures,  but  an 
appreciable  difference  from  the  values  given  in  the  table  may  be  expected 
for  large  changes  in  temperature.  When  this  value  is  expressed  in 
B.T.U.  per  pound  of  gas,  the  value  is  numerically  the  same  as  when 
expressed  in  calories  per  gram.  . 

When  heat  energy  is  added  to  a  gas  kept  at  constant 
volume,  the  temperature  and  pressure  both  increase. 
According  to  the  Kinetic  Theory,  the  heat  energy  increases 
the  mean  velocity  of  the  molecules.  The  increased  fre- 
quency with  which  they  impinge  against  the  side  of  the 
containing  vessel  as  well  as  the  increase  of  kinetic  energy 
accounts  for  the  increase  in  pressure  on  the  sides  of  the  vessel. 
The  increase  in  temperature  in  the  case  of  a  "  perfect  gas  " 
would  be  exactly  in  proportion  to  the  amount  of  energy 
added.  The  heat  capacity  or  specific  heat  of  a  gas  at 

198 


VIII.     EXPANSION  OF  GASES  199 

constant  volume  is  a  definite  quantity  for  any  gas  for  any 
fixed  range  of  temperature. 

Table  VI  gives  a  set  of  values  for  the  specific  heat  of 

gases  at  constant  volume,  and  in  each  case  gives  the  range 

of  temperature  over  which  the  value  given  is  an  average. 

S    The  Specific  Heat  at  constant  pressure  (CP)  of  a  gas  is 

~    "5bhe  heat  energy  necessary  to  increase  the  temperature  of  a 

)unit  mass  one  degree  without  a  change  of  pressure. 

V       These  definitions  are  simple  enough,  and  the  fact  that 

)  there  are  two  specific  heats  is  easily  explained.     If  a  gas  is 

/  heated  at  constant  volume  all  of  the  energy  added  goes 

into  internal  energy  of  the  gas,  or,  in  other  words,  all  of 

/   the  work  tends  to  produce  a  rise  in  temperature.     If  heat 

\    energy  is  added  at  a  constant  pressure,  however,  the  gas 

(will  increase  in  volume  while  its  temperature  is  increasing 
one  degree.  For  an  increase  in  volume  to  take  place  the 
atmosphere  or  other  restraining  body  must  be  pushed  back, 
and  consequently  work  must  be  done  against  the  opposing 
pressure  which  this  body  is  exerting.  This  work  is  external 
and  does  not  heat  the  gas.  Thus,  just  as  in  the  case  of 
latent  heat,  we  may  analyze  Cp  into  internal  and  external 
heat  energy.  To  illustrate: 

Given  1  Ib.  of  air  at  32°  F.,  held  in  a  cylindrical  piston,  similar 
to  that  in  Figs.  30  and  31,  of  1  sq.ft.  cross-section  and  indefinite 
length.  If  we  expand  it  at  a  constant  pressure  of  14.7  Ibs.  per  square 
inch  to  33°  F.  we  will  increase  its  volume  by  1/493  of  its  original 
volume.  Its  original  volume  was  12.39  cu.ft.  and,  therefore,  its 
increase  in  volume  must  have  been  1/493X12.39  =  .0251  cu.ft.  To 
free  this  volume  and  make  it  available '  for  occupancy,  energy  must 
have  been  supplied  to  move  an  area  of  144  sq.in.  through  .0251  ft. 
against  atmospheric  pressure,  or  (14.7 X 144 X. 025)  53.3  ft.-lbs.  of 
work  must  have  been  done.  (See  section  37:  72  =  53.3.)  In  B.T.U. 
the  work  done  was  53.3 -i-  780  =  .0683  B.T.U.  expended  in  doing  external 
work. 

In  addition  to  doing  the  external  work  (Cc)  .1694  B.T.U.  energy 
is  needed  to  heat  the  gas.  .1694  B.T.U.  (Co)  will  raise  one  pound 
of  air  from  32°  F.  to  33°  F.  at  constant  volume.  All  of  this  .1694 
B.T.U.  is  retained  in  the  gas  as  heat  (internal  work). 


200  HEAT 

If  we  add  these  two  quantities  of  energy  we  have,  .1694  B.T.U. 
(internal  work) +  .0683  B.T.U.  (external  work)  =  .2377  B.T.U.  total 
heat  energy  required  at  constant  pressure  for  this  1°  F.  rise. 

By  referring  to  Table  VI  for  the  specific  heat  of  gases,  the  student 
will  observe  that  the  difference  between  the  two  specific  heats  given 
represents  in  each  case  the  external  work.  It  thus  appears  that  the 
real  heat  capacity  of  the  gas  is  expressed  by  the  specific  heat  at  con- 
stant volume. 


When  heat  energy  is  added  to  a  gas  kept  at  constant 
pressure  the  volume  and  the  temperature  tend  to  increase. 
In  this  case  some  work  must  be  done  externally  if  the 
volume  is  increased  against  the  atmospheric  pressure. 
Also  work  must  be  done  internally  to  produce  the  necessary 
increase  in  the  mean  velocity  of  the  molecules  which, 
according  to  the  Kinetic  Theory,  we  expect  to  take  place. 
The  specific  heat  at  constant  pressure  is  therefore  greater 
than  the  specific  heat  at  constant  volume. 

Now  a  cause  of  much  confusion  is  the  careless  way  in 
which  some  writers  give  the  impression  that  the  energy 
added  at  constant  pressure  is  "in  the  gas."  Though 
statements  are  worded  loosely,  the  student  should  always 
remember  that  some  of  the  energy  added  to  the  gas  in  con- 
stant pressure  expansion  is  used  by  the  gas  to  do  external 
work. 

Similarly  the  expression  "  total  heat  energy  of  steam  " 
does  not  mean  that  all  of  the  B.T.U.  are  actually  in  the  steam. 
This  expression  really  gives  the  number  of  B.T.U.  required 
to  produce  the  steam  at  this  pressure  from  water  at  32°.  The 
number  of  B.T.U.  in  the  steam  is  less  than  this  value  by  an 
amount  equal  to  the  external  work  done  during  the  pro- 
duction of  the  steam. 

The  specific  heat  of  each  gas  is  different  from  that  of 
every  other  gas.  In  gas-engine  computations  and  in  com- 
putations involving  flue  gases  or  other  mixtures  of  air  and 
products  of  combustion,  it  is  usual  to  take  the  specific 
heat,  and  any  factors  depending  upon  the  specific  heat, 


VIII.     EXPANSION  OF  GASES 


201 


as  the  same  as  for  air.  Notice  that  in  Table  VI  the  value 
for  CC>2  falls  far  enough  below  that  given  for  air,  and  that 
the  value  for  N  is  enough  above  to  give  an  average  result 
equaling  the  value  for  air. 

In  the  general  formula,  PV=  RT  (see  page  90),  R 
equals  .37  when  V  is  expressed  in  cubic  feet  and  P(  in 
pounds  per  square  inch.  If  P  is  expressed  in  pounds 
per  square  foot,  R  will  equal  .37X144  (sq.in.)  or  53.37.  This 
value  for  R  can  also  be  obtained  by  expressing  the  values  of 
the  specific  heat  at  constant  pressure  and  at  constant 
volume  as  shown  in  the  following  table: 


Gas. 

Value  of 
Ratio  from 
Table  VI. 

B.T.U.  for 
1  Pound 
Raised  1°  F. 

Foot-pounds. 
1  Pound 
Raised  1°  F. 

AIR 

0 

.2375 

.2375 

184.77 

c,  * 

.1689 

.1689 

131.40 

Cp—  CD 

.0686 

.0686 

53.37 

AMMONIA 

CP 

.5084 

.5084 

395.54 

Cv 

.3500 

.3500 

272.30 

Cp—Ct 

.1584 

.1584 

123.24 

As  a  further  illustration  of  how  we  select  the  proper 
specific  heat  for  use  in  practical  computations,  the  student 
should  consider  how  we  would  find  the  energy  required  to 
superheat  10  Ibs.  of  steam  unde,r  atmospheric  pressure 
from  the  boiling-point  to  500°  F.  If  we  imagine  that 
the  steam  is  in  the  cylinder  of  Fig.  30  at  212°  F.  when  the 
heat  is  applied,  it  will  be  clear  that  the  addition  of  heat 
energy  will  tend  to  increase  the  volume  and  move  the 
frictionless  piston  up.  In  this  way  the  heat  energy  will 
do  work  against  the  atmosphere,  and  only  part  of  the 
energy  added  will  remain  in  the  gas.  The  value  in  the 
column  in  the  table  marked  Cp  must  therefore  be  used. 


202  HEAT 

Accordingly,  if  we  assume  that  the  specific  heat  is  con- 
stant, .48  (Cp)is  the  value  to  be  used,  and 

.48X10  Ibs.X (500° -212°)  =  1380  B.T.U.  of  heat  added. 

Problem  1.  Compute  the  true  specific  heat  of  sample  10, 
Table  V? 

Problem  2.  Compute  the  true  specific  heat  of  sample  ll, 
Table  V. 

Problem  3.  If  CH4  has  a  specific  heat  (Cp)  of  .593,  compute 
the  specific  heat  of  sample  8,  Table  V. 

Problem  4.  If  in  a  gas  engine  a  charge  weighing  .2  lb.,  is  at 
120  Ibs.  pressure  and  at  400  °  F.,  what  would  be  its  temperature 
after  the  explosion  of  the  gas  if  25  B.T.U.  are  released?  (Take 
value  of  specific  heat  as  given  in  table.  Assume  no  change  in 
volume.) 

Problem  5.  Make  a  tenth  column  in  Table  VI  and  compute 
and  enter  in  it  the  value  of  R  for  1  lb.  of  each  gas. 

69.  Isothermal  Expansion.  The  word  isothermal  means 
"  at  equal  temperatures,"  and  isothermal  expansion  (or 
compression)  is  any  change  in  the  pressure  and  volume  of 
a  gas  that  may  take  place  without  a  change  of  temperature. 

When  the  pressure  and  the  volume  of  a  perfect  gas  are 
assumed  to  change  without  any  change  in  temperature 
occurring  during  the  process,  the  relation  between  P  and 
V  is  expressed  by  Boyle's  Law,  PF  =  a  constant.  Generally, 
whenever  isothermal  expansion  is  assumed,  the  gases  will 
be  considered  as  approximately  obeying  Boyle's  Law. 
Thus  it  is  usually  said  that  isothermal  expansion  is  expan- 
sion in  accordance  with  Boyle's  Law.  Since  no  gas  exactly 
obeys  Boyle's  Law  and  many  gases  act  at  decided  variance 
with  it,  the  statement  that  isothermal  expansion  is  expansion 
in  accordance  with  Boyle's  Law  is  not  accurate,  but  it  ex- 
presses an  assumption  which  is  convenient  for  purposes  of 
computation.  A  convenient  way  of  writing  the  formula  is: 


VIII.     EXPANSION  OF  GASES 


203 


Fig.  55  shows  the  familiar  Boyle's  Law  curves  for  two 
temperatures,  100°  F.  and  400°  F. 

When  a  gas  under  pressure  is  allowed  to  expand,  it  must 
at  least  do  work  against  the  atmospheric  pressure  in  making 
more  volume  available  for  its  occupancy.  This  work  must 
be  done  at  the  expense  of  the  heat  energy  within  itself, 
therefore,  it  must  be  cooled.  Then  for  isothermal  expansion 
of  a  gas,  heat  energy  must  be  supplied. 


96 


80 


ISOTHERMAL  CURVES 

AND 

ADIABATIC  CURVE 
FOR  1*  OF  AIR 


8  10  J2 

Volume  Cu._Et. 

FIG.  55. 

Likewise,  if  isothermal  compression  takes  place  it  will 
be  necessary  to  do  work  upon  the  gas.  This  work  will 
appear  in  the  gas  as  heat  energy.  Therefore,  to  have 
isothermal  compression  the  gas  must  be  uniformly  cooled 
at  the  same  time  that  it  is  being  compressed. 

The  energy  given  up  by  the  gas  when  expansion  takes 
place  is  equal  to  the  pressure  on  the  outside  of  the  container 
times  the  increase  in  volume.  The  work  will  be  in  inch- 
pounds  if  the  pressure  is  expressed  in  pounds  per  square  inch 
and  the  volume  in  cubic  inches.  It  will  be  only  necessary 


204  HEAT 

to  divide  by  12  to  change  the  result  to  foot-pounds  and  by 
780  to  B.T.U.  If  the  expansion  is  to  be  isothermal  the 
energy  to  do  the  work  against  the  atmospheric  or  other 
external  pressure  must  be  supplied  to  the  gas  from  an 
external  source. 

Similarly,  upon  the  compression  of  a  gas  an  amount  of 
work  must  be  done  equal  to  the  product  of  the  decrease  in 
volume  times  the  mean  pressure  of  the  gas.  The  energy  in 
B.T.U.  will  be  equal  to  the  volume  in  cubic  inches  times  the 
pressure  in  pounds  per  square  inch  divided  by  12  and  by  780. 
If  the  compression  is  isothermal  this  energy  must  be  taken 
from  the  gas  during  the  process. 

70.  Adiabatic  Expansion.  Suppose  we  have  an  air- 
compressor  cylinder  filled  with  air,  and  suppose  that  the 
construction  of  the  cylinder  is  perfect;  that  is,  there  being 
no  leaks  by  the  piston,  no  friction,  and  the  walls  of  the 
cylinder,  as  well  as  the  piston,  being  made  of  a  non-conducting 
material.  If  the  piston  compresses  the  air  quickly,  all 
of  the  work  expended  in  moving  the  piston  is  done  on  the 
gas  and  must  be  in  the  gas  in  the  form  of  heat  energy.  Such 
a  compression  would  be  called  adiabatic  and  would  be  in 
accordance  with  the  formula: 

P(Fy)=a  constant, 
or 

Pi(V1y)=P2(V2y). 

The  exponent  y  in  this  formula  is  the  ratio  of  Cv  to  Cv  or: 

c, 


c,=y- 


Thus  y  for  air  is: 

.238 
.169 


=  1.41. 


Expansion  (or  contraction)  is  said  to  be  adiabatic  when 
it  is  in  accordance  with  this  formula. 


VIII.     EXPANSION  OF  GASES  205 

Adiabatic  expansion  would  take  place  in  the  gas-engine 
cylinder  between  the  time  of  the  explosion  and  the  opening 
of  the  exhaust  valve  if  conditions  were  ideal.  It  should 
also  take  place  in  the  steam-engine  cylinder  between  the 
cut-off  of  the  steam  and  the  exhaust  of  the  steam. 

Adiabatic  expansion  assumes: — (1)  that  a  gas  gives  up 
no  heat  energy  as  such,  but  only  as  mechanical  energy,  and 
(2)  that  it  gives  up  this  energy  at  a  given  maximum  rate 
as  called  for  by  the  formula. 

The  first  assumption  is  contrary  to  practice  because  in 
any  actual  cylinder  or  other  piece  of  apparatus,  radiation 
and  conduction  to  the  containing  walls  take  place.  Thus 
some  of  the  heat  energy  in  the  gas  is  always  transferred  to 
adjacent  bodies  as  heat  energy. 

The  second  assumption  is  approximately  fulfilled  in 
steam  engines  and  explosion  motors,  where  the  governor 
tends  to  equalize  conditions. 

There  is  some  confusion  in  the  use  of  the  term  adiabatic.  When- 
ever a  gas  expands  behind  a  piston  and  is  made  to  do  useful  work 
the  process  is  commonly  called  "  adiabatic  expansion."  However, 
true  adiabatic  expansion  implies  that  a  maximum  possible  amount  of 
work  was  done.  Whether  the  maximum  amount  of  work  is  done  will 
depend  in  any  particular  case  upon  whether  the  connected  machinery 
reacts  and  gives  a  large  enough  opposing  force. 

By  the  definition  of  a  force  we  know  that  every  action  must  have 
its  equal  reaction.  A  gas  cannot  expand  and  do  useful  work  unless 
there  is  an  opposing  force  equal  to  the  maximum  force  which  the  gas 
can  exert.  Where  the  pressure  in  the  gas  is  considerably  in  excess 
of  the  pressure  opposing  it  (friction  and  opposing  torque  of  the  con- 
nected machinery)  the  excess  pressure  in  the  gas  accelerates  the  fly- 
wheel, i.e.,  the  excess  pressure  is  balanced  by  the  inertia  of  the  fly-wheel. 

In  any  engine  which  is  provided  with  a  governor,  an  acceleration 
beyond  normal  speed  results  in  a  reduction  of  the  gas  supply  to  the 
cylinder  and  a  consequent  reduction  of  M.E.P.,  thus  equalizing  the 
opposing  forces  on  the  piston. 

No  word  is  more  often  used  in  theoretical  discussion 
of  engine  performance  than  the  word  adiabatic.  The 
student  must  remember  that  a  reference  to  an  adiabatic 


206  HEAT 

change  merely  refers  to  a  change  according  to  the  assumed 
formula.  This  formula  assumes  expansion  or  compression 
without  the  taking  or  giving  of  energy  in  the  heat  form. 
(See  Fig.  55.)  Compression,  however,  is  always  truly  adiabatic, 
that  is,  follows  the  formula  except  as  the  gas  loses  or  gains 
heat  by  radiation,  conduction  and  convection. 

Problem  6.  Suppose  a  compressor  receiving  air  at  70°  F.  were 
to  raise  the  pressure  of  air  in  one  stage  to  15  atmospheres,  what 
would  be  the  resulting  temperature? 

The  first  step  is  to  find  the  volume  of  the  air  at  15  atmospheres 
after  adiabatic  compression. 

(1)  Pi(Vi»)  =P,(  W). 

12.39  cu.ft.  =  volume  of  1  Ib.  of  air. 
(2) 


(4)  log  12.39  =  1.093. 

(5)  log  12.391-"  =  1.093X1.41  =1.541. 

(6)  log  15  =  1.176. 
Subtracting  (6)  from  (5), 

(7)  log(TV-«)=-365. 
Dividing  by  1.41, 

(8)  log  7*  =  .259. 

F2=1.82. 

The  new  volume  after  adiabatic  compression  would  therefore 
be  1.82  cu.ft.  of  air. 


1X12.39     15X1.82 


VIII.     EXPANSION  OF  GASES  207 

531X15X1.82 
Tz=     "7^39 ' 

(12)  !T2  =  11700  F.  (Absolute.) 

Or  U  =1170  -461  =  709°  F.  final  temperature. 

Problem  7.  If  an  air  motor  on  a  compressed-air  mine  loco- 
motive were  to  draw  in  air  at  75°  F.  and  135.3  Ibs.  pressure;  if  it 
were  to  have  10  per  cent  clearance  and  have  cut-off  take  place  at 
such  a  point  in  the  stroke  as  to  have  the  air  exhausted  at  .3  Ib. 
pressure  at  the  end  of  the  stroke;  find  the  point  of  cut-off  and 
temperature  of  exhaust. 

Let  Vi  =  volume  of  air  in  cylinder  after  admission; 
V2  =  volume  of  cylinder. 

Assume  adiabatic  expansion. 

(1)  Pi(7i»)  -Pi(TVO. 

(2)  1507il'««15xl.lOl>«. 

1  101'41 

(3)  K—^. 

(4)  log  1.10  =  .041. 

(5)  log  1.101>41  =  .041  xl.41  =.058. 

(6)  log  10  =  1.000. 
Subtracting  (6)  from  (5), 

.058-1.000=  -.942(9.058-10). 

(7)  log  Vi™=  -.942. 

—  Q49 

(8)  log  F^-y^  =-.668, 

or 

log  7:  =9.332 -10. 

(9)  Vi  =  .215  volume  of  air  admitted. 


208  HEAT 

Since  10  per  cent  was  the  clearance  space,  the  admission  valve 
must  have  cut  off  the  air  supply  after  the  stroke  had  progressed 
(21.5  —  10  per  cent)  11.5  per  cent  of  its  total  motion. 

do)  ^-^.  II 

^  1  12 

150X.215     15X1.1 
~535~~       ~TT 

(12)  T2=274, 

or  U  =  — 187°  F.  (temperature  of  exhaust). 

The  foregoing  problem  shows  the  result  which  might 
be  obtained  if  it  were  possible  to  run  a  motor  under  con- 
ditions giving  adiabatic  expansion  and  perfect  lubrication 
at  low  temperature. 

Problem  8.  Compressed  air  for  the  production  of  liquid  air  is 
often  used  at  a  pressure  of  3000  Ibs.  If  compression  were  to  take 
place  adiabatically  from  15  Ibs.  pressure  and  60°  F.  to  3000  Ibs. 
pressure,  what  would  be  the  resulting  theoretical  temperature? 

Problem  9.  Under  the  conditions  of  Prob.  8,  it  is  usual  to 
compress  the  gas  in  four  stages  (or  steps)  and  cool  the  air  between 
each  stage  with  cooling  water.  Would  it  seem  wise  to  you  from 
a  study  of  the  temperature  produced  in  each  stage  to  have  the 
pressure  at  the  end  of  stage  1  equal  750  Ibs.?  stage  2  equal  1500  Ibs.? 
stage  3  equal  2250  Ibs.?  What  temperature  would  adiabatic 
compression  produce  in  each  stage? 

Problem  10.  Suppose  an  ideal  air-refrigerating  machine  used 
compressed  air  at  200  Ibs.  pressure  and  60°  F.,  if  it  had  no  clear- 
ance, for  what  part  of  the  stroke  should  it  draw  air  to  exhaust 
it  at  14.7  Ibs.  pressure?  Find  the  temperature  of  the  exhaust. 

Problem  11.  Suppose  we  assume  that  we  are  to  use  an  ideal 
steam  engine  with  no  clearance,  and  we  admit  superheated  steam 
at  185.3  Ibs.  pressure  and  408°  F.  If  we  expand  this  steam 
adiabatically  to  atmospheric  pressure,  and  if  the  ratio  of  the  specific 
heats  is  1.3,  what  would  be  the  exhaust  steam  temperature?  The 
answer  will  be  found  to  be  below  212°  F.,  the  temperature  of 
saturated  steam  at  exhaust.  Account  for  this  by  explaining  what 
would  really  happen  with  steam  exhausted  as  above. 


VIII.     EXPANSION  OF  GASES  209 

Problem  12.  In  an  NH3  compressor,  the  clearance  is  filled  with 
oil  so  that  conditions  may  more  nearly  agree  with  the  ideal  adia- 
batic  conditions.  If  a  cylinder  is  compressing  against  a  back 
pressure  of  28  gauge  to  180  Ibs.,  at  what  point  of  the  stroke 
would  the  exhaust  valve  open?  What  would  be  the  theoretical 
temperature  if  the  NH3  were  at  50°  F.  before  compression? 

Problem  13.  If  the  machine  mentioned  in  Prob.  12  handled 
C02  between  350  and  800  Ibs.,  what  would  be  the  place  in  the 
stroke  where  the  exhaust  valve  opens  and  the  corresponding 
temperature,  if  the  temperature  before  compression  is  50°  F.? 

71.  Quantity  of  Energy  in  Gases.  Thus  far  in  this 
text,  only  the  pressure,  volume  and  temperature  of  a  gas 
have  been  discussed.  If  this  theory  is  to  be  applied  prac- 
tically, however,  the  quantity  of  energy  (H)  which  is  asso- 
ciated with  the  gas  under  varying  conditions  of  P,  V  and 
T  must  be  considered. 

Just  how  much  energy  we  would  have  to  take  out  of 
any  particular  gas  to  reduce  it  to  absolute  zero  we  do  not 
know.  We  have  little  hope  of  ever  finding  out,  because  we 
probably  will  never  be  able  to  reach  absolute  zero  and 
make  measurements  at  that  temperature  with  which  to 
determine  quantity  relations. 

When  we  speak  technically  of  the  quantity  of  energy 
of  steam,  we  refer  to  the  total  energy  which  must  be  added 
to  one  pound  of  water  at  32°  F.  to  change  it  into  steam  at 
the  given  temperature  and  pressure.  This  is  equal  to  the 
sum  of  the  internal  energy  plus  the  external  energy.  The 
internal  energy  is  in  turn  made  up  of  Latent  heat  and 
sensible  heat. 

Theoretically  speaking,  a  perfect  gas  should  have  asso- 
ciated with  it  a  total  amount  of  energy  above  absolute  zero 
equal  to  its  specific  heat  Cp  times  its  absolute  temperature 
times  its  weight.  Actually  the  total  heat  energy  above 
32°  F.,  EM,  associated  with  any  permanent  gas  such  as 
air,  hydrogen,  oxygen,  nitrogen,  etc.,  at  atmospheric  pres- 
sure, will  be  equal  to  its  temperature,  (F)  less  32  multi- 
plied by  its  specific  heat  (Cp),  or 


210  HEAT 


where 

and  W  =  external  work. 

The  formulae  for  the  work  done  during  adiabatic  expan- 
sion of  a  perfect  gas  are  expressed  as  follows: 


y-i 


y-l 

where      7i  =  initial  volume  in  cubic  inches; 

¥2  =  final  volume  in  cubic  inches; 

W  =  work  done  in  inch-pounds; 

PI  =  initial  pressure; 

P2=  final  pressure; 

TI  =  initial  temperature; 

T%  =  final  temperature; 
and 


Isothermal  expansion  is  expressed  by  the  following  formulae  : 


or 


or 

TT« IMP  log,  r; 

where 

R  —  Cp — Cr; 

T=the  constant  temperature; 


VIII.     EXPANSION  OF  GASES  211 

and 


If  P  is  expressed  in  pounds  per  square  inch  and  V  in 
cubic  inches,  the  work  is  expressed  in  inch-pounds.  Divid- 
ing by  12  will  change  this  quantity  to  foot-pounds,  and  to 
change  to  B.T.U.  divide  the  result  in  inch-pounds  by 
12X780. 

The  following  problem  will  illustrate  the  use  of  this 
formula  : 

Problem  14.    Find  the  work  done  per  pound  of  air  in  Prob.  7. 
The  formula  for  the  work  done  in  foot-pounds: 


y_l  • 

From  Prob.  7  we  may  obtain  the  initial  volume  in  cubic  feet 
as  follows: 

P.Fo     P,F, 

,  .  -TO v o    r\  v i 

\A)  T    "   T    ' 

14.7  X  12.39  _  150XF! 
493  536 

Vi  =1.32  cu.ft.  or  2,280  cu.ins. 

This  air  is  expanded  in  the  ratio  of  .215  to  1.1  in  the  cylinder. 
Therefore, 

F2  =6.79  cu.ft.     or    11,700  cu.ins. 

Substituting  in  (1), 


=44  B.T.U., 

the  external  work  done  by  the  compressed  air.  This  result  gives 
the  work  which  could  be  delivered  by  the  air  motor  assuming 
that  it  was  connected  to  a  suitable  load  and  that  it  worked 
adiabatically. 


212  HEAT 

72.  Reversible  Processes.  It  is  usually  stated  in  con- 
nection with  a  theoretical  discussion  of  engine  cycles  that 
all  processes  are  reversible.  The  new  idea  that  is  involved 
in  this  statement  follows  as  an  axiom,  from  the  statement 
of  the  law  of  conservation  of  energy  and  our  definition  of  a 
perfect  gas. 

If  a  pound  of  a  given  gas  has  a  pressure  PI,  a  volume 
Fi  and  a  temperature  T\,  there  is  a  perfectly  definite 
amount  of  energy  associated  with  it,  H\.  At  a  new  condi- 
tion, expressed  by  P2,  F2,  T2,  the  1  Ib.  of  gas  would  have  a 
new  and  definite  quantity  of  energy,  H2.  By  whatever  plan 
of  varying  each  factor  we  make  the  transition  to  condition 
P2,  V2,  T2,  we  will  find  that  in  the  end  the  quantity  HZ  of 
energy  is  in  the  gas.  If  we  return  to  the  condition  PI, 
FI,  Ti,  by  any  method  of  changing  P,  V  and  T  which  we 
may  choose,  we  will  find  that  the  original  quantity  HI  of 
energy  is  in  the  1  Ib.  of  gas,  whenever  its  condition  is 
expressed  by  Pi,  Fi,  T\. 

In  discussing  a  cycle  of  operations  in  a  steam  or  gas 
engine  the  condition  of  the  gas  is  indicated  by  giving  values 
to  P,  F  and  T.  Thus  the  expressions  shown  below  might 
be  used  to  show  that  a  given  mass  of  gas  passed  through 
four  distinct  conditions: 


PiFi      P2F2      P3F3      P4F4  f 

Ti  T2  '        T3  '        T4  '        Ti  '        T2  ' 

There  will  be  a  definite  quantity  of  energy  in  the  gas    at 
each  condition,  namely:  * 

Hlf    H2,    H3,    Hi,    Hlt    H2,  etc. 

Now  if  the  order  of  steps  were  reversed  and  taken  in  the 
order 

P2F2      PiFi       P4F4      P3F3      P2F2      PiFi 

T2    '       TI    '       Ti    '       Ts    '       T2    '       Ti    '        ' 


VIII.     EXPANSION  OF  GASES  213 

the  energy  in  each  case  would  be 

7/2,     Hij    H±,    Ha,    Jf/2,     #1,  etc., 

although  the  cycle  of  operations  through  which  the  gas  was 
passed  was  reversed. 

The  student  should  remember  that  these  reversible 
cycles  are  only  approximated  in  the  actual  engine.  The 
losses  due  to  friction  and  conduction  effectually  prevent 
an  actual  reversal  of  any  engine  cycle.  Every  large  engine 
uses  a  new  mass  of  working  medium  each  cycle  which 
results  in  leakage  losses.  In  a  gas  engine  the  explosion  is 
a  non-reversible  process. 

These  reasons  for  a  variation  in  the  performance  of  any 
actual  engine  from  theoretical  results  should  always  be 
borne  in  mind. 

In  order  to  obtain  the  result  in  Prob.  14  in  another  way,  suppose 
we  start  with  1  Ib.  of  air  at  135.3  Ibs.  pressure,  l.llft  cu.ft  volume, 
and  75°  F.  We  will  cool  it  at  constant  volume  to  .3  Ib.  pressure. 
The  temperature  resulting  may  be  found  from  the  formula, 


or  from  the  formula: 

(2)  *  Pt»Po(l+<rf). 

Using  formula  (1) 

150     535 

~\$~~rl' 

T2  =  53.5°F.  (absolute). 

Next  we  will  expand  it  at  constant  pressure  to  a  volume  of  5.728 
cu.ft.  The  temperature  will  then  be  274°  F.  (absolute). 

To  cool  the  gas  at  constant  volume  from  535°  F.  absolute  to  53.5°  F. 
absolute  would  involve  the  extraction  from  the  pound  of 


(535-54).169  =  81.3  B.T.U. 


214  HEAT 

To  expand  the  gas  at  constant  pressure  would  require  the  addition  of 

(Ta-Ts)^  B.T.U. 
(274-54).238  =  52.3  B.T.U. 

During  the  expansion  at  constant  pressure  external  work  would  be 
done: 


1728(6.76-1.32)15 


12X780 

Therefore  of  the  52.3  B.T.U.  returned  to  the  gas  only 
52.3-15.0  =  37.3  B.T.U. 

remained  in  the  gas  as  heat  energy.  81.3  B.T.U.  were  originally 
extracted  and  37.3  B.T.U.  returned,  therefore  the  total  energy  used 
externally  must  have  been  81.3-37.3=44.0  B.T.U. 

This  amount  agrees  with  the  result  obtained  above  by  the  formula 
for  work  done  during  adiabatic  expansion. 

Problem  15.  Find  the  external  work  done  by  1  Ib.  of  air 
initially  at  a  pressure  of  135.3  Ibs.  and  a  volume  of  1.32  cu.ft. 
during  the  expansion  to  a  volume  of  6.76  cu.ft.  at  a  constant 
temperature  of  75°  F.  (Remember  that  this  is  expansion  according 
to  Boyle's  Law.) 

Problem  16.  With  cooling  water  in  a  condenser  how  much 
energy  may  be  taken  out  per  pound  of  air  compressed  in  a  cylinder 
working  adiabatically,  without  clearance,  between  atmospheric 
pressure  and  225  Ibs.  gauge?  Assume  initial  temperature  of  air, 
and  also  of  the  circulating  water  leaving  the  condenser  through 
which  the  compressed  air  is  led,  to  be  60°  F. 

Problem  17.  If  this  air  in  Prob.  16  were  then  expanded  adia- 
batically to  atmospheric  pressure,  what  would  be  its  temperature? 
How  much  energy  could  it  take  up  in  warming  to  60°  F.  after 
adiabatic  expansion? 

Problem  18.  If  the  expansion  in  Prob.  17  had  been  into  the 
atmosphere  (or  free  as  we  say)  what  would  have  been  the  final 
temperature  and  the  amount  of  energy  absorbed  per  pound  in 
warming  to  60°  F.? 

Problem  19.  80°  F.  is  the  temperature  of  the  air  and  gas 
charge  drawn  into  the  cylinder  of  a  gas  engine  having  a  clear- 
ance of  15  per  cent.  The  cylinder  is  filled  at  a  pressure  of  14 
Ibs.  absolute.  What  will  be  the  temperature  and  pressure  when 
the  engine  is  on  dead  center  and  all  the  gas  charge  has  been 


VIII.     EXPANSION  OF  GASES 


215 


compressed  into  the  clearance?    How  much  energy  has  been  given 
to  the  gas  during  the  compression? 

Problem  20.  If  a  gas  engine  has  15  per  cent  clearance  and  after 
the  explosion  of  the  charge  the  gases  have  a  temperature  of  2200°  F. 
and  a  pressure  of  180  Ibs.,  find  the  temperature  and  pressure  of 
exhaust  and  the  work  done  during  the  working  stroke.  Assume 
adiabatic  expansion  y  =  lAO. 

73.  Entropy.  There  is  one  very  important  case  in 
which  a  number,  of  which  the  quantity  of  heat  in  a  gas 
is  a  factor,  is  numerically  used  in  a  formula  involving  pres- 
sure and  volume. 

In  adiabatic  expansion  we  have  PFw  =  a  constant. 


FIG.  56. 
A  numerical  factor  in  this  constant  is  equal  to  f  sum  -^J. 

This  sum  ^  is  called  the  entropy  of  the  substance. 

The  numerical  quantity  which  we  call  entropy  is  used 
as  a  label  to  tell  us  something  about  how  the  energy  is 
associated  with  a  substance.  The  student  will  best  learn 
what  this  word  means  by  using  the  quantity  in  the  solu- 
tion of  problems. 

A  very  good  illustration  of  the  use  of  the  quantity  in 
computation  is  offered  by  practical  problems  upon  steam  and 
steam  engines. 

TJ 

In  speaking  of  the  entropy  of  steam,  the  sum  —  is  com- 
puted for  the  quantity  of  heat  added  in  making  the  steam 


216  HEAT 

from  water  at  32°  F.  Thus  the  entropy  of  steam  is  a  func- 
tion of  the  total  heat  of  steam  as  given  in  the  steam  tables. 
Thus,  if  the  steam  was  at  32°  F.  the  only  energy  it  would 
contain  above  32°  F.  would  be  all  due  to  its  latent  heat. 
Since  this  is  all  added  at  32°  F.,  or  492°  absolute  F., 
the  entropy  would  be  the  latent  heat  divided  by  492,  or 

1072 -2  180 

w 

This  quantity  (2.180)  is  called  the  gain  entropy  during 
vaporization. 

The  entropy  of  steam  at  33°  F.  is  made  up  of  two  parts, 
the  entropy  of  the  liquid  and  the  entropy  of  vaporization. 

If  the  specific  heat  of  water  were  uniformly  1,  the  entropy 
at  33°  F.  would  be 


492.5  '   493 

The  entropy  of  the  liquid  at  212°  F.  would  be  the  sum  of 
the  series: 

1  1  1  1 

492.5  +493.5  +494.5  "*  °  671.5  ~ 

The  entropy  of  dry  saturated  steam  at  212°  F.  would  be 
the  sum  of  the  entropy  of  the  liquid  and  the  entropy  of 
vaporization,  or 

Q70 

.3125+^=1.7566. 


On  the  other  hand,  if  the  steam  contained  some  fog  and  had 
a  quality  of  only  .99,  the  entropy  of  the  steam  would  be 

.3125+.99  (1.4441)  =  1.7421. 

Thus  we  may  say  that  the  entropy  of  a  substance  is  a 
numerical  factor  which,  when  taken  in  conjunction  with 


VIII.     EXPANSION  OF  GASES 


217 


the  pressure  and  volume  of  a  substance,  tells  us  the  quantity 
of  energy  in  it. 

If  we  have  steam  under  14.7  Ibs.  pressure  and  its  entropy 
is  1.800  we  know  that  it  contains  more  energy  than  dry 
saturated  steam,  i.e.,  it  is  superheated  enough  to  give  it  an 
additional  entropy  of  .04  above  that  of  dry  saturated  steam. 
If  the  specific  heat  is  assumed  to  be  constant  and  .5,  then 
.04  equals  the  sum  of  the  series: 


.5 


.5 


-h 


+  etC'  t0 


672.5   '  673.5  '  674.5 


where  x  is  the  number  of  degrees  of  superheat. 


FIG.  57. 


Table  X  shows  the  entropy,  volume  per  pound  (specific 
volume)  quality,  pressure,  and  temperature  of  saturated 
steam  at  the  pressure  given  on  the  same  line.  While  this 
table  is  usually  called  a  Temperature-Entropy  Table,  it 
would  be  more  logical  to  call  it  a  Pressure-Entropy  table, 
for  the  horizontal  lines  simply  indicate  the  pressure  of 
the  steam  and  the  vertical  columns  the  entropy,  etc. 

Wherever  we  have  saturated  steam,  the  temperature 
for  all  qualities  will  be  as  given  in  the  first  column  of  the 
table.  If  the  steam  quality  shows  superheating,  the  quality 
plus  the  temperature  in  the  first  column  will  be  the  true 
temperature  of  the  steam. 


218  HEAT 

The  use  of  this  table  is  illustrated  by  the  following 
problems. 

Problem  21.  A  steam  engine  is  supplied  with  steam  at  205.4  Ibs. 
and  superheated  167°  F.  If  each  cylinder  had  no  clearance, 
worked  adiabatically,  and  exhausted  the  steam  against  a  back 
pressure  of  .7  lb.,  what  would  be  the  energy  left  in  the  steam 
and  the  theoretical  heat  efficiency  of  the  engine? 

By  consulting  the  table,  the  entropy  of  steam  at  220.1  Ibs. 
absolute  and  167°  superheat  is  found  to  be  1.64  and  the  total 
heat  content  1293.6  B.T.U.  In  the  1.64  column  opposite  .7  lb. 
pressure  we  find  the  quality  to  be  .8066  and  the  total  heat  content 
897.9.  The  energy  left  in  the  cylinder  would  be 

1293.6  -897.9  =395.7  B.T.U., 
and  the  efficiency  (Rankine  cycle)  is 


=33  per  cent. 


5 


It  will  be  noticed  that  the  exhaust  of  this  engine  would  contain 
nearly  2  per  cent  water  in  spite  of  a  rather  large  superheat. 


VIII.     EXPANSION  OF  GASES  219 


REVIEW  PROBLEMS,  CHAPTER  VIII 

22.  Compute  the  specific  heat  of  a  mixture  of  4  Ibs.  of  air 
and  .8  Ib.  of  CO. 

23.  If  this  mixture  burned  resulting  in  1.3  Ibs.  C02  and  3.5  Ibs. 
of  nitrogen,  compute  the  specific  heat  of  the  products  of  com- 
bustion. 

24.  If  the  weight  of  1  cu.ft.  of  hydrogen  is  .005621  Ib.,  com- 
pute the  ratio  between  C,  and  CP  at  0°  C.    Assume  that  Cp  =3.400. 
How  much  is  Cv  for  hydrogen  according  to  your  computation? 

25.  A  value  often  given  for  water  is  y  =  l.33.    Compute  and 
record  in  your  table  the  value  of  Cv. 

26.  Given  for  bromine  y  — 1.293.     Compute  and  record  hi  your 
table  the  value  of  Cp. 

27.  Given  for  chloroform  y  =  1.102.    Compute  and  record  in 
your  table  the  value  of  C0. 

28.  For  sulphuric  ether  Cp  at  40°  =  .42,  and  j/  =  1.03.     Com- 
pute Cv  and  record  its  value  in  the  table. 

29.  Compute  from  Prob.  26  and  the  tables  the  density  of 
bromine  at  147°  C. 

30.  From  Prob.  27  and  the  tables  compute  the  density  of 
chloroform  at  107°  C. 

31.  From  Prob.  28  and  the  tables  compute  the  density  of 
ether  at  137°  C. 

32.  Compute  as  in  Prob.  5,  p.  202,  the  value  of  R  for  bromine, 
chloroform,  ether,  and  water. 

33.  An  ammonia  compressor  draws  gas  at  42°  F.  and  28-lb. 
gauge  pressure.     It  discharges  the  gas  at  165  Ibs.  gauge  and  102°  F. 
Assume  that  1  cu.ft.  of  ammonia  at  32°  F.  weighs  .0476  Ib.  and 
apply  the  laws  of  a  perfect  gas  to  obtain  weights  per  unit  volume 
at  other  temperatures.     Compute  actual  work  done  upon  it. 

34.  How  much  work  would  have  been  done  in  Prob.  33  if  the 
compression  had  been  isothermal? 

35.  If  in  Prob.  33  adiabatic  compression  had  been  assumed, 
what  must  have  been  the  final  temperature? 

36.  If  adiabatic  compression  took  place  in  Prob.  33,  how  much 
work  must  have  been  done? 


220  HEAT 

37.  In  Prob.  36  at  what  point  in  the  stroke  did  the  exhaust 
valve  open? 

38.  A  triple-expansion  engine  receives  steam  under  196  Ibs. 
absolute  pressure  and  superheated  149°.     It  exhausts  into  a  low- 
pressure  turbine  which  in  turn  exhausts  into  a  condenser  against 
a  back  pressure  of  .70  Ib.     If  the  expansion  had  been  adiabatic, 
compute  the  volume  of  12  Ibs.  working  medium  as  exhausted. 

39.  Compute  the  pounds  of  steam  per  I.H.P.   per  hour  in 
Prob.  38. 

40.  How  many  B.T.U.  must  have  been  left  in  the  cylinder  per 
pound  of  steam  in  Prob.  38? 

41.  In    Prob.     13    adiabatic    compression    is   assumed;    find 
the  temperature  of  the  exhaust. 

42.  How  much  energy  must  be  taken  out  by  cooling  water  if 
1  Ib.  of  air  at  15  Ibs.  pressure  is  taken  in  at  70°  F.  and  is  to  be 
delivered  at  70°  F.  and  90  Ibs.  gauge  pressure? 

43.  If  the  compression  in  Prob.  42  had  been  isothermal,  how 
much  heat  must  have  been  taken  out  during  the  stroke?     Compare 
this  result  with  the  answer  in  Prob.  42. 

44.  A  gas  engine  has  a  clearance  of  20  per  cent.     It  draws  a 
charge  of  gas  at  a  mean  temperature  of  75°  F.    Assuming  that  this 
charge  has  the  same  physical  properties  as  air,  what  was  its  tem- 
perature when  it  had  been  adiabatically   compressed  into  the 
clearance? 

45.  In  Prob.  44  how  much  work  was  done  by  the  fly-wheel 
during  compression  per  pound  of  gas  compressed? 

46.  In  Prob.  38  what  was  the  efficiency,  assuming  the  con- 
ditions in  the  Rankine  cycle? 

47.  Using  the   formula   for   an    all-gas    cycle,    compute    the 
efficiency  and  compare  your  result  with  that  obtained  in  Prob.  46. 

48.  An  engine  works  on  the  Rankine  cycle  and  uses  steam  having 
an  entropy  of  1.64  under  200  Ibs.  pressure.    What  was  the  tempera- 
ture of  the  steam? 

49.  In  Prob.   48  what  was  the  efficiency  if  the  steam  was 
exhausted  into  a  condenser  against  a  back  pressure  of  .5  Ib.  abs.? 

60.  In  Prob.  49  compute  the  steam  consumption  in  pounds  per 
hour  per  I.H.P. 

51.  In  Prob.  49  what  would  be  the  efficiency  assuming  an  ideal 
all-gas  cycle? 

52.  Assume  the  conditions  of  the  Rankine  cycle  and  that  an 
engine  receives  dry  saturated  steam  at  a  temperature  of  340°  F. 
The  steam  is  exhausted  into  the  atmosphere.    Compute  the  B.T.U. 
left  in  the  cylinder. 


VIII.     EXPANSION  OF  GASES  221 

53.  Compute  the  efficiency  in  Prob.  52. 

54.  Compute  the  energy  left  in  cylinder  in  Prob.  52  if  a  con- 
denser in  which  an  absolute  temperature  of  1.1  Ibs.  was  maintained 
had  been  used. 

55.  Compute  the  efficiency  in  Prob.  54. 

56.  If  steam  were  used  adiabatically  in  a  compound  engine  and 
if  a. steam  trap  were  introduced  between  the  two  cylinders,  how 
much  water  could  be  drawn  off  at  the  trap  (under  perfect  condi- 
tions of  separation)  and  what  would  be  the  weight  of  water  in 
the  exhaust?     Assume  that  the  steam  entered  the  second  cylinder 
dry  and  that  both  cylinders  worked  upon  the  Rankine  cycle. 

Pressure  in  steam  main  =153  Ibs.  abs. 

Degree  superheat  =  48.7°  F. 

Pressure  at  receiver,  between  cylinders       ••=  80.0  Ibs.  abs. 
Pressure  at  condenser,  between  cylinders  =     1.47  Ibs.  abs. 

57.  In  Prob.  56  what  would  have  been  the  quantity  of  heat 
left  in  the  cylinders? 

58.  In  Prob.  56  what  would  have  been  the  efficiency? 

59.  If  in  Prob.  56  no  water  had  been  extracted  between  the 
two  cylinders,  what  would  have  been  the  efficiency? 

60.  What  would  have  been  the  efficiency  assuming    an    all- 
gas  cycle  in  Prob.  52? 

61.  What  is  the  entropy  of  1  Ib.  of  steam  containing  1280  B.T.U. 
at  208  Ibs.  absolute  pressure? 


222  HEAT 


SUMMARY,   CHAPTER  VIII 

There  are  two  specific  heats  of  a  gas.  The  numerical 
value  of  THE  SPECIFIC  HEAT  AT  CONSTANT  VOL- 
UME is  equal  to  the  quantity  of  heat  energy  necessary 
to  raise  a  unit  mass  of  the  gas  one  degree. 

The  numerical  value  of  THE  SPECIFIC  HEAT  AT 
CONSTANT  PRESSURE  is  equal  to  the  energy  required 
for  expansion  at  constant  volume  plus  the  external  work 
done  in  increasing  the  volume. 

ISOTHERMAL  EXPANSION  is  expansion  at  con- 
stant temperature. 

ADIABATIC  EXPANSION  is  expansion  tinder  a 
set  of  assumed  conditions  which  are  never  obtained 
in  practice.  These  are  that  no  energy  be  received  nor 
given  up  by  the  gas  except  energy  in  the  mechanical  form. 
True  adiabatic  expansion  implies  a  maximum  rate  of 
transfer  of  energy  and  obeys  the  formula 

Pi  Vi»  =  P2V2y  =  a  constant. 

When  the  above  formula  holds,  the  work  done 
during  adiabatic  expansion  may  be  computed  from 


. 
If-  1 

ENTROPY  is  a  numerical  factor  in  the   constant  in 
the  formula  for  adiabatic  expansion,  and  is  obtained 

TT 

by  computing 


CHAPTER  IX 

CONVECTION,   CONDUCTION,   RADIATION,   AND    THE 
INSULATION   OF   BODIES 

74.  Convection  of  Heat  Energy.  The  illustrations  of 
convection  currents  in  fluids  are  so  numerous  that  students 
in  general  are  familiar  with  the  term. 

Convection,  as  the  etymology  of  the  word  suggests, 
refers  to  the  carrying  about  of  heat  by  circulating  masses. 

Whenever  the  lower  portion  of  a  fluid  receives  heat 
energy  from  an  external  source,  a  small  portion  nearest 
the  source  becomes  warmer,  and  expanding,  grows  less  dense 
than  the  remainder  of  the  fluid. 

Therefore  the  downward  gravity  pull  upon  the  warmer, 
less  dense  fluid  becomes  less,  bulk  for  bulk,  than  that 
upon  the  surrounding  colder  fluid,  and  just  as  the  heavy 
pan  of  a  balance  is  pulled  down  thus  lifting  the  lighter  pan, 
so  the  colder  portion  of  fluid  is  drawn  down  and  the  light 
portion  forced  up.  By  this  means  currents  are  set  up 
which  tend  to  stir  the  mass  until  it  becomes  of  uniform 
temperature.  If  heating  from  the  top  takes  place,  no  such 
circulation  results,  for  the  heavy  portion  is  at  the  bottom, 
where  it  will  stay  unless  moved  by  an  external  force. 

If  we  notice  the  air  currents  in  a  steam-heated  room, 
we  find  that  cold  air  at  the  bottom  of  a  radiator  comes  in 
contact  with  the  hot  surface  of  the  metal  and  is  heated 
by  it.  The  energy  gained  by  the  gas  causes  it  to  expand 
and  its  density  to  decrease  below  that  of  the  cooler  air  in 
the  room.  The  less  dense  hot  gas  floats  up  to  the  top  just 
as  a  light  liquid,  such  as  kerosene  oil,  floats  to  the  top  of 
a  heavier  liquid,  such  as  water:  As  the  convection  currents 

223 


224'  HEAT 

rise,  the  heated  gas  may  come  in  contact  with  the  cooler 
walls  and  give  up  part  of  the  energy  gained  from  the  steam 
pipes.  As  soon  as  it  is  cooled  by  giving  up  its  heat,  this 
air  becomes  more  dense  than  the  air  which  is  being  heated 
by  the  steam  pipes.  If  the  room  is  closed,  this  dense  air 
will  drop  down  in  the  parts  of  the  room  remote  from  the 
radiator,  crowding  upward  the  warm  air  beside  the  radiator. 
After  mixing  with  other  air  it  may  again  go  over  the  steam 
pipes  and  repeat  the  trip  about  the  room. 

From  this  illustration  it  will  be  seen  that  energy  is  not 
passed  along  by  convection  currents  except  by  the  simul- 
taneous movement  of  masses  of  the  fluid.  Convection 
currents  may  occur  in  liquids  and  gases.  A  solid  cannot 
have  convection  currents  set  up  among  its  molecules  and 
accordingly  we  cannot  heat  a  solid  internally  by  convection. 

All  ventilating  and  heating  systems  for  houses,  etc., 
take  advantage  of  this  principle  to  distribute  artificial  heat 
about  in  each  room.  The  hot- water  system,  and  the  hot- 
air  furnace  system  also  depend  upon  convection  to  convey 
the  energy  from  the  furnace  to  the  several  rooms  to  be 
heated.  Our  winds,  in  most  cases,  are  nothing  more  than 
convection  currents  on  a  large  scale. 

In  the  steam  boiler,  the  convection  currents  play  a  very 
important  part.  In  the  boiler  shown  in  Fig.  40,  the  heating 
of  the  water  in  the  water  tubes  not  only  expands  the  water 
and  diminishes  the  density  of  the  water,  but  also  causes 
some  steam  to  form.  The  density  of  the  mixture  is  very 
much  less  than  that  of  the  water  at  any  temperature.  The 
water  in  the  rear  water  leg  A,  being  more  dense,  settles, 
moving  the  mixture  of  water  and  steam  up  in  the  front 
head  B,  and  from  there  back  into  the  boiler.  The  proper 
action  of  the  boiler  is  dependent  upon  so  constructing  the 
tubing  and  headers  that  the  convection  currents  will  pro- 
duce a  rapid,  continuous  circulation. 

This  force,  which  moves  the  mass  of  fluid  upward  when 
convection  currents  are  established,  is  due  to  the  difference 


IX.     CONVECTION  225 

between  the  weight  of  the  column  of  hot  fluid  and  that 
of  a  cold  column  of  equal  length  and  cross-section.  Thus 
the  force  which  is  tending  to  move  the  air  up  the  chimney 
in  Fig.  61  would  be  computed  as  follows: 

The  height  of  the  chimney  is  100  feet. 

The  temperature  of  the  gases  in  the  chimney  is  600°  F. 

The  temperature  of  the  outside  air  is  75°  F. 

The  weight  per  cubic  foot  at  75°  is 

Tl     Di  461  X.  0864 


and  similarly  the  weight  at  600°  F.  =  .0375. 

The  difference  in  weight  per  cubic  foot  =  .0367.  There- 
fore this  difference  times  100  gives  the  moving  force  per 
square  foot  of  cross-section  at  the  base,  or  .0367X100  =  3.67. 
The  moving  force  in  pounds  per  square  inch  would  equal 

^=.025. 
144 

In  practice  a  draft  gauge  is  used  to  measure  this 
force.  This  is  simply  an  open-arm  manometer  such  as  the 
student  has  used  to  measure  the  pressure  of  the  gas  in  the 
laboratory.  The  difference  in  pressure  on  the  two  sides 
of  the  U  tube  causes  the  water  to  stand  one  inch  higher 
on  the  side  communicating  with  the  chimney  for  every 
.036  Ib.  of  pressure.  Therefore  the  ,  difference  in  pressure 
between  the  atmosphere  and  the  inside  of  the  chimney 
will  be  measured  by  the  number  of  inches  on  the  draft 
gauge  times  .036  Ib. 

The  Draft  of  a  Chimney.  The  velocity  of  the  gases 
issuing  from  the  chimney  depends  upon  so  many  factors 
that  most  engineers  rely  upon  tables  based  upon  experience 
to  supply  the  data  from  which  to  design  new  stacks. 

The  preceding  problem  explains  the  draft  of  a  chimney. 


226  HEAT 

Theoretically  the  velocity  of  the  gases  coming  out  of  the 
chimney  would  be  as  expressed  by  the  following  formula: 


where  V  =  velocity; 

ft  =  the  difference  between  the  height  of  the  chimney 
and  the  height  to  which  a  column  of  gas  of  the 
same  length  and  cross-section  area  as  the  chim- 
ney would  extend  if  heated  from  the  tempera- 
ture of  the  outside  air  to  the  temperature 
of  the  chimney; 
y  =  the  acceleration  due  to  gravity. 

The  actual  formulae  in  use  are  based  more  upon  experi- 
ence than  theory.  (See  any  handbook.) 

75.  Conduction  of  Heat  Energy.  Conduction  is  very 
different  from  convection.  For  instance,  if  heat  energy  is 
supplied  to  one  end  of  a  metal  rod  the  energy  is  passed 
on  from  layer  to  layer  until  it  reaches  the  other  end.  If 
you  stick  a  metal  rod  of  any  convenient  length,  such  as  1  ft., 
in  the  fire  and  hold  the  other  end  in  the  bare  hand  it 
very  quickly  becomes  uncomfortably  warm. 

When  heat  energy  is  transferred  from  one  part  of  a  body 
to  another,  without  motion  of  integral  parts  of  the  body, 
intervening  parts  being  also  heated,  the  process  is  called 
conduction. 

Instead  of  using  one  rod  let  the  student  select  two  rods, 
one  of  copper  and  the  other  of  iron,  each  of  like  dimensions, 
such  as  J  in.  in  diameter  and  24  ins.  in  length,  and,  holding 
one  in  each  hand,  let  him  place  an  end  of  each  rod  in  the 
forge  fire.  The  heat  from  the  fire  will  be  conducted  through 
the  metal  to  the  hand  and  the  copper  rod  will  be  too  hot 
to  hold  while  the  iron  rod  is  still  cold.  The  rate  of  transfer 
differs  for  each  solid  material,  but,  in  general,  it  is  true 
that  good  electrical  conductors  are  also  good  heat  conductors. 

The  process  may  best  be  understood  by  thinking  of  the 
molecular  structure  of  the  body  and  the  Kinetic  Theory. 


IX.     CONDUCTION  227 

We  may  think  of  each  circular  section  of  the  copper  rod 
as  consisting  of  a  sheet,  1  molecule  of  copper  in  thickness. 
When  the  end  is  thrust  into  the  fire  the  molecules  in  the 
end  section  are  quickly  heated  and  have  their  kinetic  energy 
(or  MV2)  greatly  increased.  The  increase  in  the  energy  of 
the  molecules  in  this  section  results  in  their  impinging  against 
the  molecules  of  the  next  adjacent  section  with  greater 
velocity  and  much  of  the  newly  added  energy  of  the  molecule 
of  the  first  section  is  transferred  to  the  second  during  the 
impact.  Thus  the  mean  velocity  of  the  molecules  is  in- 
creased from  layer  to  layer  outward  from  the  source  of 
heat  at  a  rate  dependent  upon  the  nature  of  the  material. 

To  gain  a  better  understanding  of  the  conditions  con- 
trolling the  rate  of  transfer  of  heat  by  conduction  let  us 
assume  a  set  of  conditions.  Suppose  a  conducting  sheet  of 
uniform  thickness  separates  a  region  of  high  temperature  t\ 
from  a  region  of  lower  temperature  £2-  A  quantity  of  heat 
energy  Q  will  be  conducted  through,  which  will  depend  upon 
the  following  factors: 

1.  The  quantity  passing  through  the  conductor  will  be 
in  direct  proportion  to  the  area  A  of  the  conductor.     In 
this  case  just  as  in  a  water  pipe  the  greater  the  area  of 
the  section  through  which  the  flow  takes  place,  the  larger 
the  volume  which  may  flow.     It  follows  that 

QocA. 

2.  The  rate  of  flow  through  the  conductor  will  depend 
upon  the  difference  in  temperature 'between  the  two  sides. 
This    difference    may   be   compared    to    the    difference    in 
pressure  which  forces  a  stream  of  water  through  a  length  of 
pipe.     No  flow  can  take  place  through  the  pipe  without  a 
difference  in  pressure. 

It  does  not  follow,  however,  that  the  amount  of  flow  is  in 
direct  proportion  to  the  difference  in  temperature,  although 
this  is  usually  assumed  in  the  case  of  a  heat  conductor. 

It  follows  that 


228  HEAT 

3.  The  amount  of  flow  will  decrease  as  the  length  of  the 
path  increases.     It  is  usually  assumed  that  the  quantity 
of  energy  transferred  is  inversely  as  the  thickness  of  the 
conductor.     Here   again  the   conditions   are   analogous   to 
those  in  a  water  pipe.     The  greater  the  length  the  less  the 
flow  under  a  given  set  of  conditions  of  size  of  pipe   and 
pressure. 

It  follows  that  Q  oc  — — ; -. 

thickness 

4.  The  amount  of  flow  depends  upon  a  constant  factor, 
K,  which  expresses  the  effect  of  the  kind  of  material  used 
and  the  ability  of  that  particular  material  to  conduct  heat. 

5.  The  total  amount  of  flow  depends  upon  the  time, 
which   is   usually   expressed   in   seconds  when   the   metric 
system  of  units  (incorrectly  but  commonly   called  in  this 
case  C.G.S.  units)  is  used,  and  in  hours,   minutes,  or  sec- 
onds, when  the  English  system  is  used. 

It  follows  that  Q  oc  time. 

These  controlling  factors  when  combined  give  us  the 
result 

KxAX(t1-t2)Xtime 
Thickness 

Or  if  K  be  given  a  proper  value  to  correspond  with  the 
units  of  size,  length,  temperature,  and  time  which  are  to 
be  substituted, 

o 


Thickness 

From  this  equation  a  value  for  K  may  be  found. 

There  are  two  common  ways  of  expressing  K,  the  "Con- 
ductance," or  the  coefficient  of  conductance  as  it  is  called 
in  most  reference  and  text-books,  as  follows : 

Coefficient  of  conductance  (metric  units)  = 

Calories  per  sec.  X thickness  in  cms. 

"Area  of  surf  ace  Jn   sq.  cms.  X  temp,  difference   in  deg.  C. 


IX.     CONDUCTION  229 

Coefficient  of  conductance  (British  units)  = 

B.T.U.  per  hr.  X thickness  in  inches 

Area  of  surface  in  sq.ft.  X difference  in  temp,  in  deg.  F. 

Or,  in  other  words,  the  conductance  has  been  given 
usually  either  as  calories  per  second  through  a  centimeter 
cube  or  as  B.T.U.  per  hour  through  a  square  foot  section 
1  in.  thick. 

There  is  a  close  analogy  between  the  conduction  of  heat 
energy  through  the  material  and  the  conduction  of  electrical 
energy  through  a  material.  Thus  a  third  way  of  measur- 
ing conductance  has  arisen.  If  the  difference  in  pressure  of 
the  heat  energy  is  the  difference  in  temperature  (c)  at  the 
two  ends,  the  current  of  heat  energy  may  be  measured  in 
watts,  and  the  resistance  to  flow  of  heat  in  " thermal  ohms" 
and  the  conductance  in  "  thermal  mhos."  * 

Using  these  terms,  we  might  say  that  for  a  square 
centimeter  cross-section  and  a  centimeter  length, 

=  thermal  ohms, 


watts 

where  t\  and  t%  are  the  temperatures  centigrade, 
or 

ti—t2  =  watts X thermal  ohms, 

^dif  ° =  watts  X  thermal  ohms. 

*  These  units  have  been  suggested  by  Carl  Hering,  Past  President 
of  the  American  Institute  of  Electrical  Engineers,  in  the  following 
articles : 

Flow  of  Heat  through  Bodies;    Metallurg.  &  Chem.  Eng.     Dec., 

1911,  p.  652. 
Flow  of  Heat  through  Bodies;    Metallurg.  &  Chem.  Eng.     Jan., 

1911,  p.  14. 
Thermal  Resistance  and  Conductivity;    Metallurg.  &  Chem.  Eng. 

Jan.,  1911,  p.  13. 
Simplification  of  Electrical  Calculations;  Proceedings  of  A.  I.  E.  E. 

June,  1912. 

In  these  articles  it  is  pointed  out  that  the  true  C.G.S.  unit  of 
conductance  would  be  an  erg  per  sec.  through  a  cm.  cube. 


230  HEAT 

The  thermal  conductance,  or,  as  it  is  frequently  called, 
the  coefficient  of  conductivity,  is  the  reciprocal  of  the 
thermal  ohm  and  is  called  the  thermal  mho.  It  is  the  product 
of  the  difference  in  temperature  between  any  two  sections 
1  cm.  apart  and  the  watts  passing  through  a  centimeter 
cube  of  material  between  these  sections. 

Temp,  difference  =  thermal  ohms  X watts. 

A  serious  limit  is  placed  upon  the  usefulness  of  this 
formula  by  the  fact  that  the  resistance  is  not  constant  for 
any  substance.  The  thermal  resistance  of  some  metals 
increases  with  the  temperature.  Other  metals  decrease  in 
resistance  with  increase  in  temperature.  Still  other  metals 
act  irregularly.  As  an  example  of  this,  iron,  according  to 
one*writer,  has  a  resistance,  in  thermal  ohms  of  approximately 
1.2  at  0°  C.,  1.1  at  100°  C.,  and  1.9  at  275°  C.  There 
is  also  a  great  deviation  in  values  given  by  various  investi- 
gators. This  requires  that  a  determination  of  the  value  of 
the  thermal  ohm  be  made  for  each  practical  computation. 

Following  the  electrical  analogy,  the  thermal  ohms 
resistance,  R,  for  any  body  of  other  than  unit  dimensions 
would  be 

«-*, 

where  r  is  the  resistance  of  the  substance  under  unit  con- 
ditions, I  the  length  of  the  path  through  which  the  heat 
flows,  and  a  the  area  of  the  path. 

There  are  two  large  fields  for  the  use  of  the  conductance, 
K,  in  practical  computations.  First,  the  insulation  of 
refrigerating  plants,  piping  and  boilers.  Second,  the  con- 
struction and  insulation  of  furnaces  and  high-temperature 
apparatus. 

The  constant  is  determined  in  the  first  type  of  problem, 
using  the  materials  under .  as  nearly  the  same  conditions 


IX.     CONDUCTION  231 

during  the  test  as  pertain  in  practice.  In  that  case  the 
coefficient  is  not  necessarily  a  true  value  for  the  particular 
materials  in  use,  but  will  express  the  effect  of  other  limiting 
conditions.  Computations  of  this  character  are  usually  in 
the  British  system. 

In  the  case  of  extremely  high  temperatures  the  con- 
ductance, K,  may  be  computed  from  practical  tests  of  the 
material  under  working  conditions  just  as  in  the  case  of 
low-temperature  insulation.  In  this  event  the  true  con- 
ductance is  not  usually  found,  but  a  coefficient  which  is 
affected  by  the  peculiar  conditions  under  which  the  material 
is  to  be  used  and  the  test  is  taken.  Computations  with  a 
factor,  K,  gained  thus  will  be  fairly  accurate.  For  electric 
furnaces  it  is  most  convenient  to  find  K  in  thermal  mhos. 

The  practical  value  of  a  true  coefficient,  K,  is  somewhat 
limited  by  the  fact  that  in  most  cases  the  heat  must  pass 
from  a  fluid  on  one  side  of  the  substance  to  a  fluid  on  the 
other  and  the  rate  of  flow  through  the  contact  surfaces 
apparently  does  not  obey  the  law  which  applies  to  solids. 
However,  problems  of  the  character  shown  below  are 
frequently  worked  out,  assuming  that  the  flow  takes  place 
in  accordance  with  the  general  law. 

K  has  the  same  general  significance  in  either  system  of 
units,  but  it  has  a  different  numerical  value  in  each  system. 
This  difference  in  value  is  due  to  the  difference  in  size  of 
the  units  of  area,  thickness,  temperature,  and  time  used  in 
each  case. 

See  Table  XIV  for  approximate  values  of  K. 

An  average  piece  of  wrought  iron  may  be  said  to  have  a  resistance 
in  thermal  ohms  of  1.2  at  0°  C.  If  its  conductance  is  wanted  in 

thermal  mhos  it  will  be  —  or  .83. 

If  the  conductance  (or  the  coefficient  of  conductivity)  in  metric 
units  is  desired  it  may  be  computed  as  follows: 

Assume  a  difference  of  temperature  between  the  two  opposite 
faces  of  a  centimeter  cube  to  be  1°  C.,  then  from  the  above  statement 
it  follows  that  .83  watt  will  flow  through  this  cube  per  second.  Now, 


232  HEAT 

there  are  4.19  watts  in  one  calorie.     Expressed  in  calories  the  flow 

OO 

through  this  cube  will  be  —  —  =  .20. 
4.19 

If  the  conductance  is  to  be  expressed  in  B.T.U.  per  square  foot 
per  hour  for  a  1°  F.  difference  in  temperature  and  a  1-in.  thickness 
there  are  five  factors  which  must  be  considered: 

First.  1°  C.  =  |  °  F.  Therefore,  the  flow  would  be  less  through  the 
section  and  it  will  be  necessary  to  multiply  the  .20  calories  by  -f  . 

Second.  1  sq.ft.  =929  sq.cms.  Therefore,  there  will  be  929  times 
greater  flow  through  a  square  foot  section  than  through  a  square 
centimeter  section.  It  is  necessary  to  multiply  by  929. 

Third.     1  in.  =2.54  cms.     Since  the  quantity  must  flow  through 

2.54  times  the  thickness  there  will  be  only  -  of  the  flow. 

Fourth.  rhr.=3600  sees.  There  will  be  3600  times  the  quantity 
flow  in  an  hour. 

Fifth.     252   calories  =  1    B.T.U.     To   change   the   quantity   from 
calories  to  B.T.U.  it  is  necessary  to  divide  by  252. 
Thus, 

.20X5X929X3600 
9X2.54X252 

Problem  1.  Lead  is  stated  by  one  author  to  have  a  coeffi- 
cient of  conductivity  of  .084  in  metric  units.  What  is  the  con- 
ductivity in  thermal  mhos  and  the  resistance  in  thermal  ohms? 

Since  one  calorie  is  equivalent  to  4.18617  watts,  and  both 
units  state  the  energy  passing  through  a  centimeter  cube,  all 
that  is  necessary  is  to  multiply  by  4.186  to  convert  calories  per 
second  into  watts. 

.084  X4.19  =.344  thermal  mho. 
1  -H.  344  =2.08  thermal  ohms. 

Problem  2.  A  second  author  states  that  lead  has  a  coefficient 
of  287  B.T.U.  per  square  foot  per  hour  per  degree  F.  Convert  to 
thermal  mhos  and  thermal  ohms. 

To  change  this  to  watts  per  centimeter  cube  per  degree  centi- 
grade difference  in  temperature, 

9        287X252X4.19 


The  resistance  =  6.  13  thermal  ohms. 


IX.     CONDUCTION  233 

Problem  3.  Suppose  a  sheet  of  \  in.  copper  (.27  thermal  ohm) 
were  to  have  one  side  in  contact  with  water  under  120  Ibs.  pressure 
and  the  other  in  contact  with  gases  at  1500°  F.,  what  would  be 
the  resulting  evaporation  per  hour  per  square  foot  of  surface? 

(Assume  feed  water  to  be  at  the  boiler  temperature.) 

S,150o    350)X27X2.54X3600X144_ 
9(  4.19X252 

This  problem  shows  conclusively  that  boiler  tubing  never 
reaches  a  temperature  of  the  same  order  as  that  of  the  gases  in 
contact  with  it. 

Problem  4.  What  would  the  results  in  Prob.  2  be  in  watts 
per  inch  cube  and  in  resistance  per  inch  cube? 

Problem  5.  Kent's  Handbook  gives  silver  as  having  a  con- 
ductivity of  1000  in  B.T.U.  per  degree  F.  per  square  foot  area 
per  inch  of  thickness  (British  system).  What  would  this  con- 
ductivity be  in  the  so-called  "  C.G.S.  units  "? 

Problem  6.  If  sawdust  has  a  coefficient  in  British  units  of  .4, 
what  is  the  weight  of  the  ice  melted  per  day  in  an  80x40x40 
ice-house  through  a  thickness  of  8  ins.  if  the  outside  temperature 
is  80°  F.?  Disregard  melting  at  top  and  bottom. 

40  X40X80X  .4  X  (80 -32) 

144X2000X8  =2' 

Problem  8.  What  would  be  the  evaporation  of  water  per  hour 
per  square  foot  through  a  boiler  plate  of  \  in.  iron,  if  the  tem- 
perature difference  were  100°  F.  and  if  the  coefficient  of  con- 
ductivity in  British  units  were  160? 

Problem  9.  If  a  boiler  has  12  ft.  of  mean  boiler  surface  for 
each  H.P.  of  boiler  rating,  and  if  the  boiler  tubing  is  .12  in.  thick, 
what  difference  in  temperature  exists  betwoen  the  two  surfaces  of 
the  tubing? 

Problem  10.  What  would  be  the  temperature  difference  in 
Prob.  9  if  the  tubing  had  been  copper? 

Problem  11.  What  would  have  been  the  difference  in  tem- 
perature in  Prob.  9  if  the  tubing  had  been  brass  (conductance 
in  C.G.S.  units  =  .265)  and  if  the  boiler  were  working  at  a  50  per 
cent  overload? 

Problem  12.  Compute  the  constants  to  convert  thermal 
conductance  from  "  C.G.S."  units  to  British  units  and  record  in 
your  book. 


234  HEAT 

76.  Insulation.  There  are  two  ways  of  considering  the 
flow  of  heat  through  bodies  by  conduction.  When  one 
speaks  of  the  ease  of  flow  he  measures  the  effect  in  terms 
of  the  unit  of  conductance,  the  thermal  mho  (or  the  coeffi- 
cient of  conductivity).  When  one  thinks  of  the  reverse 
effect,  the  resistance  of  the  material  to  flow,  he  will  measure 
the  property  of  the  material  in  " thermal  ohms,"  which  are 
obtained  by  taking  the  reciprocal  of  the  thermal  mhos. 
The  choice  of  term  depends  upon  the  use  to  which  we  put 
the  material.  Copper  tubing  is  introduced  into  a  boiler  so 
that  heat  energy  may  be  conducted  through  the  walls  of  the 
tube  to  the  water  within  as  quickly  as  possible.  In 
English  locomotives,  the  firebox  is  often  made  of  copper 
because  it  is  the  best  cheap  metallic  conductor  of  heat  and 
accordingly  permits  a  greater  amount  of  steam  to  be  made 
per  square  foot  of  surface  exposed  to  gases  than  would  any 
other  material.  We  then  say  that  copper  is  a  good  con- 
ductor, and  in  such  instances  would  measure  the  flow  of 
heat  in  terms  of  thermal  mhos. 

We  cover  the  outside  of  boilers  with  lagging  in  order 
to  keep  heat  from  being  conducted  away.  Here  we  want  a 
poor  conductor  of  heat  and  we  say  we  have  used  an 
"  insulator."  The  property  by  virtue  of  which  it  resists  'the 
flow  of  heat  would  be  measured  in  thermal  ohms. 

These  terms  are  similarly  used  in  electricity. 

Sawdust,  charcoal,  asbestos,  and  various  other  porous 
materials  are  in  very  common  use  to  prevent  the  con- 
duction of  heat  away  from  warm  bodies  or  into  refrigerating 
piping,  cold  storage  rooms,  ice  houses,  and  the  like.  These 
are  used  because  they  all  fill  the  first  of  the  following  set  of 
requirements  for  a  good  insulator.  The  common  materials 
in  use  for  this  purpose,  besides  being  cheap,  should  have  low 
heat  conductivity,  should  be  non-inflammable,  mechan- 
ically strong  enough  to  stand  handling,  vibration,  and 
heat  fluctuations,  chemically  constituted  so  that  they  do  not 
corrode  or  decompose  when  subjected  to  heat  and  moisture. 


IX.     INSULATION  235 

A  light,  porous  material  that  entangles  a  large  amount 
of  air  within  itself  is  specially  good,  provided  that  it  does 
not  have  single  spaces  large  enough  to  allow  convection 
currents.  Enclosed  air  is  a  very  bad  conductor.  Asbestos 
forms  a  part  of  most  laggings,  and  besides  being  used  alone 
is  frequently  used  to  bind  together  other  insulating  com- 
pounds of  magnesium,  carbonates,  various  silicates,  etc. 

While  these  materials  make  the  conduction  of  heat  slow, 
even  better  results  are  obtained  if  the  outside  is  painted  to 
give  it  a  glazed  surface. 

Conduction  from  a  solid  surface  to  an  adjacent  layer 
of  fluid  is  greater  from  a  matt  surface  than  from  a  smooth 
surface. 

Problem  13.  A  refrigerator  box  has  an  area  of  1000  sq.ft. 
Its  walls  are  8  ins.  thick  and  have  a  conductance  of  2.2  B.T.U. 
The  temperature  is  to  be  kept  at  30°  F.  when  the  external  tem- 
perature averages  80°  F.  for  24  hours.  What  would  be  the  B.T.U. 
per  hour  conducted  away? 

Problem  14.  A  refrigerator  is  made  up  of  layers  of  material 
in  the  following  order: 

|  in.  matched  pine  boards; 

Damp-proof  paper: 

1  in.  matched  boards; 

2-in.  joists  providing  a  space  which  is  filled  with  sawdust; 

f-in.  matched  boards; 

Waterproof  paper; 

f-in.  matched  boards; 

2-in.  joists  to  make  an  air-space; 

f-in.  matched  boarding; 

Damp-proof  paper: 
and      £-in.  matched  boarding. 

What  would  be  the  conductance  of  the  combination?  (Neg- 
lect the  paper.)  The  resistance  of  the  whole  wall  is  the  sum  of 
the  resistances  of  each  layer  of  material.  There  are  six  thick- 
nesses of  f-in.  boards  and  their  combined  thermal  resistances  are 
as  follows: 

1  in.  X6  X2700  =  14,180  thermal  ohms. 

The  thermal  resistance  R  of  2  ins.  of  sawdust  is 
2  X 1560  =  3120  thermal'  ohms. 


236  HEAT 

The  thermal  resistance  of  2  ins.  of  air  is 

2  X2000  =4000  thermal  ohms. 

Adding  these  quantities,  we  have  21,300  thermal  ohms  as  the 
total  resistance. 

Problem  15.  What  loss  per  hour  will  result  from  the  storage 
of  liquid  air  in  a  glass  vessel  YG  m-  thick  of  1  sq.ft.  area  of  surface, 
if  the  outside  were  at  20°  C.  and  the  inside  at  - 180°  C.?  Explain 
why  this  result  does  not  really  agree  with  practice. 

Problem  16.  A  refrigerator  has  a  single  glass  window  of 
4  sq.ft.  area.  If  the  inside  is  at  36°  F.  and  the  outside  at  70°  F., 
what  ice  loss  is  produced  thereby  per  day? 

Problem  17.  What  would  be  the  conductance  in  British  units 
in  Prob.  14? 

Problem  18.  A  steam  main  carrying  steam  at  200  Ibs.  pressure 
in  a  room  at  75°  F.  has  a  total  area  of  lagging  of  168  sq.ft.  If 
the  lagging  is  2  ins.  of  magnesia  having  a  resistance  of  1400 
thermal  ohms  per  centimeter  cube  per  degree  centigrade,  what  is 
the  B.T.U.  loss  per  hour  for  the  entire  length? 

Problem  19.  What  weight  of  ice  in  melting  would  absorb  the 
added  energy  due  to  the  heating  through  brine  pipes  lagged  with 
a  total  area  of  200  sq.ft.  of  2  ins.  thick  asbestos  with  a  conduc- 
tivity in  C.G.S.  units  of  .00030?  Difference  in  temperature  between 
the  brine  and  air  85°  F. 

77.  Radiation.  It  has  already  been  stated  on  pages  7 
and  8  that  radiation  is  due  to  a  wave  motion  and  that 
this  wave  motion  is  always  accompanied  with  a  giving  of 
energy  by  the  body  emanating  the  rays.  When  the  body 
is  very  hot  the  wave  motion  affects  our  eye  and  we  call 
it  light.  Even  though  we  do  not  see  the  rays  it  is  true 
that  all  bodies  are  giving  off  energy  in  wave  form.  We  have 
all  experienced  the  blistering  effect  of  these  waves  which 
come  from  regions  of  temperature  below  700°  C  as  we  have 
stood  about  bonfires.  They  pass  through  a  vacuum  without 
heating  it,  i.e.,  without  loss  of  energy,  and  there  are  many 
substances  such  as  hard  rubber  and  glass  which  allow 
certain  of  these  rays  to  pass  through  without  greatly  heating 
the  medium.  The  energy  radiated  from  the  sun  in  clear, 


IX.     RADIATION  237 

dry  weather  is  transmitted  through  the  atmospheric  air  to 
the  earth  with  very  little  loss.  These  radiations  come 
through  the  region  of  air  100  miles  in  depth  with  a  loss 
which  has  been  estimated  as  less  than  20  per  cent  under 
the  most  favorable  conditions. 

The  wave  length  is  the  distance  from  the  crest  of  one 
wave  to  the  crest  of  the  next  wave.  This  length  is  the 
same  as  the  distance  between  the  similar  parts  of  any  two 
adjacent  waves. 

Radiations  are  often  discussed  under  three  different 
topics :  Light,  ultra-violet  light,  and  heat  radiations.  These 
rays  are  all  alike  in  character  and  differ  from  one  another 
only  in  wave  length  and  amplitude.  If  one  were  to  heat  a 
piece  of  iron  to  400°  F.,  the  wave  lengths  would  be  not  longer 
than  140  millionths  of  a  centimeter.  One  could  not  see  any 
light  rays  coming  from  the  iron,  but  he  could  feel  the  heat 
rays  without  touching  it.  Heat  the  iron  further  to  about 
975 °F.  and  there  would  be  a  few  rays  as  short  as  80  millionths. 
The  eye  will  begin  to  be  affected  by  these  radiations  and  will 
record  a  faint  red  color.  Other  colors  are  seen  about  as 
follows : 

Dull  red  1300°  F.  =  (a   larger   quantity   of   80 

millionth  wave  lengths) 
Cherry  from  1500°  to  1800°  F.  =  (65    millionths    length    in 

quantity) 
Orange  from  2000°  to  2200°  F.  =  (55    millionths    length    in 

quantity) 
White  from  2350°  up  =  (50    millionths    length    in 

quantity) 
Dazzling  from  2700°  up  =  (45    millionths    length    in 

quantity) 

At  just  what  temperature  ultra-violet  rays  (of  less  than 
40  millionths)  begin  to  be  produced  by  a  hot  body  is  not 
so  definitely  shown,  but  they  are  present  in  considerable 
quantity  in  the  radiation  from  a  body  at  2500°  F.  While 


238  HEAT 

the  eye  sees  by  means  of  the  rays  between  80  and  40,  the 
ultra-violet  rays,  of  length  shorter  than  40,  affect  the  sensi- 
tive material  on  the  photographic  film  and  it  is  only  by  means 
of  the  camera,  spectroscope,  radiometer,  bolometer,  and 
such  delicate  instruments  that  we  may  study  such  rays.  The 
greater  part  of  the  energy  radiated  by  all  sources  of  light 
mentioned  in  Table  XII  is  in  the  form  of  the  long  wave 
length  heat  radiations.  The  ultra-violet  rays  take  away 
only  a  very  small  per  cent  of  the  energy  of  even  such  very 
hot  bodies  as  the  arc  lamp.  The  glass  globe  of  an  arc  lamp 
screens  them  effectually.  Strong  ultra-violet  rays  produce 
very  bad  flesh  burns  which  are  difficult  to  heal. 

There  is  a  mercury  vapor  arc  lamp  which  has  found 
occasional  use  in  Europe  which  operates  at  an  extremely 
high  temperature  and  must  therefore  be  enclosed  by  a 
quartz  tube.  Since  quartz  transmits  ultra-violet  rays  and 
since  this  lamp  emits  an  unusual  quantity  of  these  rays, 
it  has  been  found  necessary  always  to  inclose  the  arc  with  a 
second  globe  of  glass  to  avoid  burns. 

78.  Radiation  Laws.  " NEWTON'S  LAW  OF  COOLING" 
states  that  the  rate  of  loss  of  energy  from  a  body  is  in  direct 
proportion  to  the  difference  between  its  temperature  and 
that  of  its  surroundings. 

To  illustrate  this,  suppose  that  the  crucible  used  in 
obtaining  the  data  for  Fig.  22  had  been  allowed  to  cool  to 
the  room  temperature.  If  Newton's  law  holds  true,  the 
rate  of  loss  would  have  been  twice  as  great  when  the  crucible 
was  100°  hotter  than  the  room  than  when  it  was  50°  hotter. 
When  the  temperature  reached  50°  it  would  take  twice  as 
long  to  cool  1°  as  it  took  at  100°.  Similarly,  at  25°  the 
rate  of  loss  would  be  only  one-fourth  of  that  at  100°. 
Accordingly  the  time  would  be  four  times  as  long  at  25°  as 
at  100°. 

When  there  is  a  considerable  difference  in  temperature 
the  law  does  not  hold.  It  is  not  even  approximately  true 
under  conditions  such  as  obtained  while  the  data  was  taken 


IX.     RADIATION  239 

from  which  Fig.  22  was  constructed.  In  this  figure  the  curve 
is  almost  a  straight  line.  This  is  due  to  the  fact  that  the 
rate  of  loss  is  much  more  nearly  uniform  .under  these  con- 
ditions than  would  be  possible  if  the  law  held  true.  The 
law  actually  holds  true  for  differences  of  temperature  not 
exceeding  20°  C.  Other  than  for  this  range,  however,  there 
is  no  law  which  applies  to  the  energy  loss  of  any  body 
subjected  to  radiation,  conduction,  and  convection  losses 
simultaneously. 

To  compute  the  radiation  losses  from  a  body  under  ideal  condi- 
tions or  "black  body"  it  is  customary  to  use  the  following  formula, 
which  is  known  as  the  Stefon-Boltzmann  Law  : 


where  E  =  ihe  total  energy; 
.K"  =  a  constant; 
TI  =  absolute  temperature; 
TI  =  temperature  of  surroundings. 

This  law  may  be  applied  to  any  body  subject  to  radiation  losses 
only.  The  amount  of  energy  lost  in  any  practical  case  will  be  in 
proportion  to  a  constant  K,  which  must  express  the  effect  of  the  nature 
of  the  surface  from  which  energy  is  being  radiated.  The  energy  loss 
with  any  given  body  will  be  in  proportion  to  the  fourth  power  of  its 
absolute  temperature.  The  energy  received  from  its  surroundings  will 
be  in  proportion  to  the  fourth  power  of  absolute  temperature  of  the 
surroundings.  Thus  the  net  rate  of  loss  of  energy  will  be  equal  to  a 
constant  times  the  difference  between  the  fourth  powers  of  the  absolute 
temperature  of  a  body  and  of  the  absolute  temperature  of  its  sur- 
roundings. 

79.  Black  Body  Radiations.  The  technical  term  "absolute  black 
body"  refers  to  an  ideal  surface  which  acts  as  a  perfect  radiator  or 
absorber  of  heat.  It  is  possible  to  construct  a  piece  of  apparatus 
which  will  give  the  same  results  as  would  an  "absolute  black  body" 
and  such  an  arrangement  is  called  a  "black  body." 

Theoretically,  the  requirements  for  a  "black  body"  are  all  met 
by  arranging  to  have  the  radiations  come  through  a  small  open- 
ing in  a  box  kept  at  constant  temperature,  from  a  lampblack  surface 
in  the  center  of  the  box.  Fig.  58  shows  such  an  arrangement. 

Suppose  an  insulated  box  be  constructed  as  shown  in  Fig.  58  and 
the  outside  packed  with  ice.  If  A  is  a  blacked  surface  in  the  middle 


240 


HEAT 


of  the  box  the  amount  of  radiations  coming  to  it  must  equal  the 
radiations  from  it  if  the  temperature  is  to  be  constant.  If  A  were  a 
perfect  black  body  it  would  absorb  all  the  radiations  from  the  walls 
C,  D,  E,  F,  etc.,  and  then  give  off  the  energy  again  in  new  radiations. 
If,  on  the  other  hand,  the  surface  A  is  not  perfect,  it  will  reflect  those 
rays  which  are  not  absorbed  and  the  total  light  coming  from  it  will 
be  the  same.  The  nature  of  the  surfaces  in  this  case  makes  no  differ- 
ence in  the  amount  of  the  radiations. 

A  lampblack  surface  very  closely  approaches  the  " black  body"  as 
an  efficient  radiating  surface.  At  ordinary  temperatures  rough  sur- 
faces radiate  better  than  smooth  polished  ones  and  glass  much  better 
than  smooth  metallic  surfaces.  A  copper  surface  painted  with  "alu- 


FIG.  58. 

minium"  flake  paint  is  found  to  radiate  much  better  than  the  bare 
polished  surface  of  the  copper  vessel. 

80.  Relation  of  Visible  Radiations  to  Heat  Radiation.  At  low 
temperatures  there  are  phosphorescent  effects,  in  which  light  waves 
are  given  off  without  an  attendant  large  loss  of  energy  in  the  form 
of  heat  radiations.  Notable  cases  of  this  in  nature  are  seen  in  fish, 
sea- water,  and  the  firefly. 

In  artificial  illumination  there  have  been  many  attempts  to  trans- 
form energy  with  apparatus  at  low  temperatures,  but  no  one  has  yet 
found  and  applied  the  firefly's  secret.  The  "  Moore  Tubes "  and 
other  vacuum  tubes  are  the  best  attempts  that  have  thus  far  been 
found  practicable.  The  temperatures  in  the  region  of  the  discharge 
are  probably  above  400°  C.,  but  since  there  is  so  small  a  mass  of  gas 
being  heated  it  is  not  easy  to  determine  the  temperature. 

In  all  of  the  so-called  incandescent  lamps  high  temperatures  are 
necessary  to  efficiency.  What  is  desired  is  to  have  the  largest  possible 
amount  of  energy  given  off  in  the  form  of  visible  rays  of  short  wave 


IX.     RADIATION 


241 


length.  Now  it  has  been  found  by  experiment  that  the  energy  given 
off  by  a  body  at  fairly  high  temperatures  is,  in  the  main,  given  off 
by  radiations  of  a  limited  range  of  wave  lengths.  This  range  of  wave 
lengths  in  which  energy  is  given  off  at  maximum  rate  (or  at  which 
rays  of  maximum  intensity  are  being  given  off)  changes  the  value  of 
the  absolute  temperature.  (See  Table  XIII.) 

Wein's  Law  is  as  follows:  "As  the  temperature  increases,  each 
wave  length  in  the  spectrum  diminishes  in  such  a  manner  that  the 
product  of  the  wave  length  and  the  absolute  temperature  is  constant." 
The  formula  for  this  may  be  written: 

XT  =  a  constant, 
where  X  =  wave  length  and  T  =  absolute  temperature. 


Per  Cent  Energy 

i-*  >->  to  to  to  co 

010-OOtOOOK-OOtO 

RELATION 
PER  CENT 
Itt  VISIBLE 
Al* 
TEMPEF 

BETWEEN 
DF  ENERGY 
SPECTRUM 
D 
ATURE 

I 

/ 

1 

/ 

/ 

/ 

/ 

/ 

Wave  Length 

FIG.  59. 


1000   2000   3000   4000   5000    6000 
Teinp.Fahrenheit 


FIG.  60. 


This  law  applies  to  each  of  the  wave  fengths  and  may  therefore 
be  applied  to  the  wave  length  of  maximum  intensity.  That  is,  it 
may  be  applied  to  the  wave  length  at  which  energy  is  being  given 
off  at  maximum  rate,  therefore, 

^ma.xT  =  a  constant. 

This  same  idea  is  better  conveyed  by  an  inspection  of  the  curves 
in  Fig.  59,  which  show  the  energy  radiated  per  second  by  bodies  at 
different  temperatures  and  shows  the  intensity  or  quantity  for  the 
various  wave  lengths.  The  area  inclosed  by  the  curves  and  the  X  axis 


242  HEAT 

line  is  in  direct  proportion  to  the  energy  given  off  per  unit  area  of  the 
radiating  body  per  unit  of  time. 

It  will  be  noticed  from  this  curve  that  the  higher  the  temperature 
the  larger  the  relative  area  in  the  visible  part  of  the  spectrum.  Apply- 
ing this  conclusion  to  the  practical  problem  of  incandescent  illumination 
it  follows  that  the  higher  the  temperature  at  which  a  lamp  is  operated 
the  greater  will  be  its  efficiency.  The  function  of  such  a  light  is  to 
transform  its  heat  energy  into  radiant  energy  of  a  limited  range  of 
wave  length. 

Carbon  lamp  filaments  may  be  operated  at  very  high  temperatures, 
but  above  1900°  C.  the  rate  at  which  the  carbon  sublimes  is  so  great 
that  it  is  not  practicable  to  use  the  higher  temperatures.  The  sub- 
limate is  deposited  on  the  glass  bulb  and  soon  blackens  the  lamp 
if  the  lamp  is  operated  at  too  high  a  voltage  and  temperature.  Tan- 
talum and  tungsten  do  not  sublime  below  their  melting-point,  so  that 
they  may  be  operated  at  higher  temperatures  than  carbon  and  there- 
fore are  more  efficient  as  lamps, 

81.  Insulation  Devices.  The  problem  of  keeping  cold 
things  cold  and  hot  things  hot  has  always  been  a  live  one. 
In  cooking  it  is  necessary  that  the  food  be  maintained  at  a 
definite  temperature  for  a  given  time  until  certain  bacterial, 
mechanical  and  chemical  changes  have  taken  place  in  the 
structure  and  composition  of  the  food.  It  formerly  was 
true  that  no  one  thought  much  about  the  heat  which  is 
lost  from  cook-stoves.  So  common  has  been  the  practice 
of  using  the  stove  for  both  heating  and  cooking  that  an 
"  insulated  stove  "  has  only  lately  begun  to  be  a  marketable 
article. 

We  now  have  "  fireless  cookers  "  in  which  food  pre- 
viously heated  to  the  cooking  temperature  is  placed.  The 
device  is  provided  with  insulation  to  prevent  loss  of  heat 
by  the  vessel  in  which  the  cooking  is  taking  place.  An 
early  form  known  as  the  "  hay  cooker  "  was  made  from  a 
box  or  pail  padded  on  the  inside  with  a  hay-filled  lining. 
After  the  covered  dish  containing  the  food  was  placed 
inside,  another  pad  was  placed  on  top  of  the  dish  and  a 
close  fitting  cover  added  to  make  a  tight  joint  between  the 
lining  at  the  side  and  the  top  pad.  This  crude  form  has 


IX.     INSULATION 


243 


proved  unsatisfactory  for  cooking  many  articles,  because  the 
success  of  the  operation  depends  upon  preventing  a  drop  of 
more  than  a  very  few  degrees. 

Electric  and  gas  "  fireless  stoves  "  are  now  being  intro- 
duced in  which  the  insulated  chamber  receives  enough  heat 
from  the  resistance  coils  or  from  a  gas  flame  to  equalize  the 
losses  of  heat  through  the  insulation.  Very  hot  soapstones 
are  also  introduced  in  some 
cookers  to  provide  a  store  of 
energy  from  which  to  supply  the 
losses  without  cooling  the  food. 

To  store  liquid  air,  Professor 
Dewar  constructed  a  glass  flask 
with  a  double  wall.  He  ex- 
hausted the  air  from  between 
the  walls  and  silvered  the  inner 
surfaces  of  the  vacuum  chamber. 
The  vacuum  prevents  convection 
and  conduction  through  what 
would  normally  be  an  air-space. 
The  only  conduction  loss  is  from 

the  top,  where  the  inner  and  outer  walls  join.  The  silver 
produces  a  mirror  surface  on  the  cold  inner  wall  and 
reduces  radiation  to  a  minimum.  The  gallon-size  Dewar 
bulbs  will  keep  liquid  air  for  two  weeks  or  more.  The 
construction  is  shown  in  Fig.  61. 

Commercial  forms  of  this  flask  variously  known  as 
"  Thermos  bottles,"  "  vacuum  bottles,"  etc.,  are  in  com- 
mon use. 


FIG.  61.— Dewar  Bulb. 


244  HEAT 


REVIEW  PROBLEMS,  CHAPTER  IX 

20.  Good  practice  allows  approximately  1  Kw.  per  square  foot 
to  be  transmitted  through  an  iron  boiler  tubing  |  in.  thick.     What 
difference  in  temperature  must  exist  between  the  two  surfaces? 

21.  Good  practice  in  condenser  tubes  allows  a  maximum  of 
\  H.P.  per  square  foot  to  be  absorbed.     What  thickness  between 
the  two  surfaces  must  exist? 

22.  107°  C.  steam  gives  up  .073  Kw.  per  square  foot  through 
a  bronzed  cast-iron  pipe  to  air  at  20°  C.     What  was  the  apparent 
thermal  resistance  of  this  material  if  it  was  \  in.  thick? 

23.  153°  C.  steam  gives  up  .170  Kw.  per  square  foot  per  hour 
through  cast  iron  to  air  at  20°  C.     What  was  the  apparent  thermal 
conductance  of  this  material? 

24.  The  conductance  of  pasteboard  is  given  as  .00045  in  cm. 
cube — calorie— degree  C  units  (C.G.S).     Compute  the  coefficient 
in  British  units. 

25.  Compute  the  conductance  in  Prob.  24  in  thermal  mhos. 

26.  Compute  the  thermal  resistance  in  Prob.  25. 

27.  Disregarding  the  effect  of  frost  and  assuming  that  the  air 
in  contact  with  the  surface  is  at  the  temperature  of  the  mass  of 
air  on  the  outside,  compute  the  B.T.U.  lost  per  hour  through  a 
plate-glass  window  f"  thick  and  8'  Xl2'    in    area.    Temperature 
inside  70°  F.     Temperature  outside  0°  F. 

28.  Kent's  Hand-book  gives  the  conductance  for  asphalt-cork 
composition  at  32°  F.  as  .484  B.T.U.  per  hour.     Compute  the 
conductance  in  thermal  mhos. 

29.  Enter  the  value  given  in  Prob.   28  for   asphalt-cork  in 
Table  XIV  and  compute  the  other  constants. 

30.  Ground  cork  is  given  by  Kent  as  having  .250  B.T.U.  per 
pound   conductance.     Record   it   in  Table  XIV,  computing  the 
proper  value  to  go  in  each  column. 

31.  Compute  the  heat  lost  per  square  foot  of  area  per  degree 
F.  difference  in  temperature  through  a  wall  made  up  as  follows: 
If  ins.  matched  boards,  4  ins.  of  ground  cork,  If  in.  matched  boards. 
Neglect  the  effect  of  paint,  tarred  paper,  etc.,  which  would  regularly 
be  used  in  this  construction  work. 

32.  Kent's  Hand-book  shows  six  values  of  the  conductance  in 
British  units  of  asbestos.    The  value  at  32°  F.  =1.048,  at  212°  F. 

=  1.346,  at  392°  F.  =1.451,  at  572°  F.  =1.499,  at  752°  F.  =1.548, 
and  at  1112°  F.  =  1.644. 

Plot  a  curve  showing  the  effect  of  temperature  on  the  con- 
ductance of  asbestos.    State  what  this  curve  shows. 


HEAT  TRANSFER  245 


SUMMARY,    CHAPTER  IX 

There  are  two  processes  by  which  heat  energy  as 
such  may  be  transferred. 

1st.  CONVECTION,  in  which  a  part  of  a  m  ass 
of  fluid  receives  energy  by  conduction,  then  the 
mass  with  its  heat  energy  is  carried  to  a  new  location 
by  currents  which  are  set  up,  and  finally  gives  up 
the  heat  to  a  colder  body. 

2d.  CONDUCTION,  in  which  the  heat  is  passed  on 
from  adjacent  layer  to  adjacent  layer  of  particles  without 
any  relative  motion  of  the  masses  of  which  the  body 
is  composed. 

ti-t2  /     pressure  . 

—  =  thermal  ohms  I  -     —7- —  =  resistance 

watts  \quantity  rate 


thermal  ohms 


'thermal  mhos  (conductance). 


There  are  three  ways  of  giving  the  constant  from 
which  conducted  heat  may  be  computed. 

In  thermal  mhos  (unit  of  conductance) . 

In  C.G.S.  units  (usually  referred  to  as  coefficient 
of  conductivity). 

In  British  units  (also  referrecl  to  as  coefficient  of 
conductivity) . 

RADIATION  is  a  process  in  which  the  energy  is 
transferred  as  an  ether  vibration. 

INSULATION  of  bodies  is  undertaken  to  pre- 
vent the  transfer  of  heat.  Poor  conductors  are  used. 
A  vacuum  is  a  perfect  preventative  for  conduction, 
and  convection.  Radiation  is  reduced  by  having  a 
mirror  surface  on  the  body  to  be  protected. 


CHAPTER  X 
FUNCTION  OF  THE  REFRIGERATOR  PLANT 

82.  Household  Refrigeration.  The  student  already 
knows  that  the  simple  plan  of  using  ice  is  the  cheapest 
and  most  common  way  of  keeping  small  quantities  of 
perishables  cool.  There  are  two  requirements  only.  First, 
an  insulated  compartment  in  which  to  store  the  goods, 
and  second,  an  adequate  supply  of  ice.  The  heat  entering 
the  chamber  is  taken  up  by  the  ice.  The  added  heat 
energy  causes  the  ice  to  melt.  Ice  is  usually  supplied  at 
its  freezing-point,  32°  F.,  therefore  every  144  B.T.U.  which 
reach  the  ice  melt  a  pound  of  it.  The  resulting  water 
which  contains  the  heat  flows  away  in  the  waste  pipe. 
The  metal  or  tile  lining  is  usually  several  degrees  above 
the  temperature  of  the  ice,  and  so  each  pound  of  water 
takes  up  a  few  more  B.T.U.  from  the  walls  of  the  chamber 
before  it  passes  out. 

Thus  if  the  temperature  of  the  water  was  40°  as  it  left 
the  refrigerator  and  the  ice  as  introduced  was  at  30°  F.,  we 
would  compute  the  heat  taken  from  the  cold  chamber  per 
pound  of  ice  as  follows : 

The  specific  heat  of  ice  =       .46 

Heat    taken  up    in    rising    from 

30°  F.  to  32°  F.  .46X2 

.92  B.T.U. 

Latent  heat  taken  up  =  144  B.T.U. 

Sensible  heat  of  water  above  32°  F.  =     8  B.T.U. 


Total  =153  B.T.U. 

246 


X.     FUNCTION  OF  THE  REFRIGERATOR  PLANT      247 

If  the  heat  gained  were  all  conducted  into  the  refrigerator, 
then  the  amount  of  heat  entering  would  be  in  proportion 
to  the  difference  in  temperature  between  the  outside  and  the 
inside.  This  is  not  the  case,  however,  as  cracks  and  the 
drain  pipe  always  allow  a  chance  for  some  convection  cur- 
rents to  bring  in  warm  air.  There  are,  also,  losses  due  to 
the  heat  added  while  articles  are  being  moved  in  or  out 
of  the  storage  space,  and  to  changes  in  humidity.  These 
irregular  conditions  make  it  difficult  to  compute  the  losses 
in  advance,  with  accuracy. 

By  computing  the  heat  absorbed  by  the  ice  or  refrigerat- 
ing machinery  under  varying  conditions,  the  losses  may 
be  analyzed. 

83.  Mechanical  Refrigeration.  Most  mechanical  re- 
frigerating plants  are  so  arranged  that  heat  is  continually 
withdrawn  from  the  cold-storage  room  by  the  evaporation 
of  an  extremely  volatile  liquid.  In  other  words,  the  body 
or  room  to  be  cooled  continually  supplies  heat  to  evaporate 
a  cold  volatile  liquid  which  is  continuously  supplied  by  the 
refrigerating  plant.  The  latent  heat  of  vaporization  is 
not  quite  all  of  the  heat  added  to  this  volatile  liquid,  because 
its  boiling-point  is  usually  so  low  that  some  sensible  heat 
is  added  to  the  gas  formed  by  the  evaporating  liquid  after 
evaporation  has  taken  place. 

The  way  this  is  accomplished  is  illustrated  by  Fig.  62, 
which  shows  a  so-called  compression-type  refrigerating  plant. 
A  steam  power  plant  is  shown,  the  steam  engine  of  which  is 
driving  the  ammonia  compressor.  The  compressor  is  doing 
mechanical  work  upon  the  cool  ammonia  and  compressing  it 
to  175  Ibs.  pressure.  This  would  result  in  a  very  hot  gas 
leaving  the  compressor  if  measures  were  not  taken  to  keep 
the  compressor  cool.  It  is  necessary  to  water-jacket  the 
compressor  to  keep  the  cylinder  from  being  overheated  by 
the  gases.  These  hot  gases  are  next  led  to  the  condenser. 
Here  they  pass  through  tubes  which  are  cooled  by  circulating 
water.  Since  the  ammonia  is  under  high  pressure,  the  boil- 


248 


HEAT 


tUD 

1 


X.     FUNCTION  OF  THE  REFRIGERATOR  PLANT     249 

ing-point,  and  consequently  the  point  of  liquefaction  is  at  a 
very  much  higher  temperature  than  under  atmospheric 
pressure.  The  condenser  water  cools  the  ammonia  to  its 
point  of  liquefaction.  After  the  water  has  taken  out  the 
latent  heat  and  changed  the  ammonia  to  a  liquid,  the  water 
cools  the  ammonia  further  until  it  has  nearly  reached  the 
temperature  of  the  circulating  water.  By  this  process  the 
heat  is  really  taken  out  of  the  refrigerating  plant  and  carried 
away. 

This  fairly  cool  liquid  might  still  be  further  cooled  by  the  use  of 
an  interchanges  The  interchanger  would  be  inserted  in  the  piping  at 
TK  and  the  piping  from  the  evaporator  coils  RM  would  be  rearranged 
to  allow  the  cool  gases  coming  from  the  evaporator  to  pass  upward  over 
pipes  TK  containing  the  liquid  ammonia  under  pressure.  The  cold 
gases  would  take  up  some  of  the  sensible  heat  of  the  liquid  entering 
the  evaporator  and  thus  increase  the  heat  absorbed  in  the  evaporator 
per  pound  of  liquid  circulated. 

In  the  evaporator,  the  liquid  under  175  Ibs.  pressure  is 
allowed  to  pass  through  the  valve  at  K  into  the  expansion 
coils  in  the  brine  tank  (or  freezing  vat.)  The  compressor 
suction  keeps  these  coils  fairly  well  freed  from  gaseous 
ammonia  so  that  a  pressure  of  about  28  Ibs.  gauge  is  main- 
tained. The  boiling-point  at  this  pressure  is  very  much 
reduced,  so  that  the  liquid  quickly  evaporates,  taking  its 
latent  heat  from  itself  and  the  adjacent  metal.  This  vaporiza- 
tion cools  the  ammonia  and  the  adjacent  piping  to  approx- 
imately 15°  F.  If  the  piping  were  made  of  a  perfect 
insulating  material,  the  liquid  would  hot  all  change  to  a 
gas,  but  a  part  would  merely  be  cooled  to  its  boiling-point  at 
28  Ibs.  pressure,  15°  F.,  by  the  evaporation  of  the  remainder 
of  the  liquid.  Actually,  the  piping  is  a  good  conductor  of 
heat  and  is  usually  in  contact  with  brine,  so  that  the  liquid 
is  all  quickly  changed  to  gas.  The  gas  itself  in  most  plants 
takes  on  enough  heat  to  raise  its  temperature  several  de- 
grees above  its  boiling-point  before  it  leaves  the  evaporator. 

In  Fig.  62  the  gas  is  shown  to  be   returned   directly 


250  HEAT 

to  the  compressor.  If  we  could  replace  the  ammonia 
with  a  liquid  which  could  be  purchased  cheaply  and  which 
could  be  allowed  to  evaporate  into  the  air,  we  would  not 
need  any  parts  in  a  refrigerating  plant  other  than  an 
evaporator.  The  escaping  gas  would  then  carry  away 
the  heat  in  precisely  the  same  way  that  the  waste  water 
carries  the  heat  from  an  ordinary  ice  chest. 

We  will  see  in  the  following  section  how  it  is  possible 
to  avoid  any  waste  of  ammonia  and  still  have  the  energy 
carried  away  through  the  waste  pipe  of  the  condenser  and 
thus  conveyed  away  from  the  plant. 

84.  Energy  Flow  through  a  Refrigeration  Plant.  In 
Fig.  63  is  shown  the  energy  flow  through  a  50-ton  (of  ice 
per  day)  plant.  The  computation  is  based  upon  the  energy 
flow  per  ton  of  ice  produced.  By  reference  to  the  diagram 
it  will  be  seen  that  166  Ibs.  of  coal  of  13,620  B.T.U.  per 
pound  energy  content  would  be  required  to  deliver  the 
63  H.P.  hours  of  mechanical  energy  required  to  make  a 
ton  of  ice.  This  energy  is  used  to  compress  the  ammonia 
sucked  out  of  the  evaporator.  In  the  compressor,  a  very 
large  quantity  of  oil  is  used  to  fill  the  clearance.  We 
might  expect  to  have  adiabatic  compression  so  far  as  the 
space  available  for  the  gas  affects  the  action,  for  we  have 
no  clearance.  If  the  exhausted  gases  were  compressed 
adiabatically  they  would  leave  at  a  rather  high  temperature 
and  at  a  pressure  of  175  Ibs.  The  presence  of  so  much  oil 
and  the  fact  that  the  walls  are  kept  cold  by  the  water 
jacket  prevents  any  considerable  rise  in  temperature 
and  more  nearly  isothermal  compression  results.  Since  no 
internal  heat  is  added  during  isothermal  expansion,  the 
work  done  is  decreased  by  the  use  of  a  water  jacket  and 
consequently  the  efficiency  of  the  cycle  is  increased.  The 
diagram  shows  145,000  B.T.U.  carried  away  in  the  jacket 
water  and  oil. 

From  the  compressor,  the  gas  is  conducted  (first  through 
an  oil  separator  which  is  not  shown  and  then)  to  the  con- 


X.  FUNCTION  OF  THE  REFRIGERATOR  PLANT  251 


6.000  B.T.U. 
taken  up  by 
Return  Piping 


-  344, 000  B.T.U. 
=Heat  removed  from 

Water  by  Ammonia 

86,000  B.T.U. 
"Heat  taken  up  by 

Ammonia  through 

leakages  in  freezing 

vat  insulation 

451,000  B.T.U. 
Removed  by 
Condenser 


145,000  B.T.U. 
Removed  by 
Compressor 
Water  Jacket 


1,051,000  B.T.U. 
]•: x im ust  Steam 


160,000  B.T.U. 
To  Run  Feed  Pumps 


66,000  B.T.U 
"Radiation  from 

Boiler 

55,000  B.T.U 
?          Boiler  Setting, 

Leakage  and  Radiatiom 


FIG.  63.— Energy  Diagram  for  Fig.  62. 


252  HEAT 

denser.  Here  it  is  cooled  to  its  saturation  temperature  at 
160  Ibs.  pressure,  liquefied  and  cooled  below  the  boiling- 
point.  This  is  accomplished  by  taking  out  the  sensible 
heat  in  the  superheated  gas,  its  latent  heat  of  vaporization, 
and  some  of  the  sensible  heat  of  the  liquid.  In  all,  451,000 
B.T.U.  are  so  taken  out.  This  quantity  of  heat  leaves 
the  plant  at  this  point  in  the  circulating  water  which  is 
thrown  away. 

In  the  evaporator  coils,  into  which  the  liquid  ammonia 
next  goes,  the  latent  heat  of  fusion  is  taken  out  of  the  water 
and  given,  through  the  walls  of  the  piping,  to  the  ammonia 
to  supply  its  latent  heat  of  vaporization.  In  leakage  losses, 
and  in  useful  work,  we  have  a  total  of  430,000  B.T.U. 
extracted  from  the  freezing  vat.  The  gaseous  ammonia 
starts  back  toward  the  compressor  at  a  temperature  of  15° 
F.  and  receives  roughly  6000  B.T.U.  which  are  conducted 
or  radiated  in  through  the  piping. 

The  exact  manner  in  which  the  energy  is  evicted  from 
the  plant  (or,  speaking  non-technically,  the  way  the  cold 
is  produced)  is  by  arranging  for  the  circulating  water  to 
carry  away  heat  from  the  condenser  and  compressor.  The 
evaporator  or  the  freezing  vat  can  absorb  only  a  limited 
amount  of  heat,  namely  the  quantity  that  the  liquid 
ammonia,  delivered  to  the  evaporator,  can  absorb  in 
evaporating  and  circulating  out  as  a  gas.  The  ammonia, 
which  is  used  over  and  over  again,  therefore,  merely 
carries  the  heat  from  the  evaporator  to  a  more  con- 
venient and  economical  point  to  reject  it,  namely  to  the 
condenser. 

85.  The  Steam  Cycle  and  the  Ammonia  Cycle  Compared. 
It  will  be  seen  from  the  foregoing  discussion  that  the  ammonia 
goes  through  a  cycle,  time  after  time,  which  much  resembles 
that  of  the  water  in  our  Figs.  29  and  30.  We  have  a  con- 
denser which  serves  the  same  purpose  in  both  cases.  We 
have  an  evaporator  in  Fig.  62  which  does  a  very  similar 
service  to  that  performed  by  the  steam  boiler  in  Fig.  29. 


X.     FUNCTION  OF  THE  REFRIGERATOR  PLANT    253 

Finally,  we  have  a  compressor  cylinder  much  like  the 
engine  cylinder  of  Fig.  29. 

The  latent  heat  of  vaporization  and  the  sensible  heat  of 
the  gas,  due  to  its  being  superheated,  are  taken  out  in  the 
ammonia  condenser.  The  only  points  of  difference  between 
the  action  of  the  ammonia  condenser  and  that  of  the  steam 
condenser  are,  first,  that  the  pressure  is  much  higher  in  the 
former  than  in  the  latter;  second,  that  the  temperature  is 
much  lower  in  the  ammonia  condenser;  and  third,  super- 
heated ammonia  gas  instead  of  a  wet  mixture  of  steam  and 
water  is  liquefied. 

In  the  ammonia  evaporator,  the  liquid  has  the  latent 
heat  of  vaporization  added  just  as  in  a  steam  boiler  water 
has  its  latent  heat  added.  The  liquid  not  only  boils,  pro- 
ducing a  saturated  gas,  but  the  gas  is  also  superheated 
either  by  passing  through  the  warmer  piping  in  the  evaporator 
or  by  the  piping  of  the  circuit  returning  to  the  compressor. 
The  steam  boiler  in  a  small  plant  usually  starts  with  the 
liquid  far  below  the  boiling-point  and  does  not  superheat 
the  steam.  Thus  the  function  of  each  piece  is  the  same, 
but  they  work  at  different  temperatures  and  pressures. 
The  range  of  temperature  relative  to  the  boiling-point  is 
different  for  the  two.  The  liquid  in  the  steam  boiler  is 
purified  and,  because  of  the  change  of  pressure,  undergoes 
a  change  in  boiling-point,  In  the  evaporator  the  liquid 
is  admitted  through  a  valve  with  a  reduction  of  pressure 
and  a  consequent  lowering  of  the  boiling-point. 

The  action  in  the  compressor  cylinder  is  the  reverse 
of  that  which  takes  place  in  the  steam  cylinder.  In  the 
engine,  hot  gas  admitted  under  high  pressure  does  work, 
expands  doing  more  work,  and  is  exhausted  as  a  wet  mixture 
at  a  reduced  temperature  and  pressure.  In  the  ammonia 
compressor,  ammonia  at  a  low  pressure  has  work  done 
upon  it  which  results  in  a  gas  being  delivered  by  the  com- 
pressor at  an  increased  pressure  and  temperature. 

While  the  direction  of  flow  of  the  working  medium  in 


254  HEAT 

the  refrigerating  cycle  is  the  same  as  that  of  the  steam  cycle 
in  the  power  plant,  the  pressure  changes  are  in  a  reverse 
order. 

The  conditions  are  almost  reversed  in  the  two  plants 
in  respect  to  the  energy  relations  throughout  the  cycle.  In 
the  steam  plant  the  object  is  to  add  all  of  the  energy 
possible  to  the  working  medium  in  every  part  of  the  plant 
save  one,  the  engine,  where  it  is  intended  to  give  out 
as  much  as  possible.  In  the  refrigerating  plant  the 
object  is  to  keep  energy  from  entering  the  working 
medium  and  to  reject  it  from  the  working  medium  as 
much  as  possible  in  every  member  except  the  evaporator, 
where  the  working  medium  is  allowed  to  receive  as  much 
energy  as  possible. 

The  steam  plant,  in  other  words,  conserves  energy  in 
its  function  of  transforming  energy  and  the  refrigerating 
plant  does  work  in  order  to  give  off  energy  in  as  large 
quantities  as  possible. 

In  the  compressor  cylinder,  just  as  in  the  engine  cylinder, 
adiabatic  conditions  would  result  if  perfection  could  be 
attained.  Therefore  the  first  steps  in  computing  the 
theoretical  performance  of  a  compressor  is  to  apply  the 
formula  for  adiabatic  compression  to  the  cylinder.  Oil 
is  used  in  the  cylinder  to  fill  the  clearance  at  the  end  of  the 
stroke  and  thus  enable  the  compressor  to  discharge  very 
nearly  all  of  the  gas  drawn  in  during  the  suction  stroke. 
The  effect  of  the  oil  and  the  water  jacket  is  to  keep 
the  working  medium  cooler  than  the  temperature  which 
would  result  from  adiabatic  compression.  The  cooler 
gas  does  not  produce  as  much  pressure  as  would  result 
from  adiabatic  compression.  Accordingly  the  engine  that 
drives  the  compressor  will  not  have  to  supply  as  great 
a  force  to  compress  the  gas,  and  it  will  therefore  do  less 
work  per  pound  of  working  medium.  Whatever  saving 
of  work  follows  from  doing  less  than  would  be  required 
under  adiabatic  conditions  also  results  in  a  second  saving 


X.     FUNCTION  OF  THE  REFRIGERATOR   PLANT    255 

to  the  plant.  If  the  energy  per  pound  given  to  the  gas  is 
reduced,  the  condenser  is  not  required  to  take  out  so  much 
energy  while  changing  a  pound  of  gas  to  liquid.  The 
condenser  will  then  have  less  work  to  do  and  can  be 
built  smaller. 

86.  Computation.  Since  mechanical  refrigeration'  com- 
petes with  ice  it  is  usual-  to  compute  the  efficiency  of  a  plant 
by  stating  its  ice-making  capacity  under  given  conditions. 
The  basis  of  the  computations  of  the  duty  and  performance 
of  a  refrigerating  plant  is  usually  the  production  of  one  ton 
of  ice.  This  is  true  whether  the  plant  is  used  for  ice-making 
or  for  any  other  purpose. 

For  example,  so-called  "  sharp  freezers "  are  rooms 
used  to  quickly  cool  and  freeze  food  products  like  fish, 
meats,  etc.,  which  are  to  be  kept  for  a  long  time  or  shipped 
long  distances.  For  these  rooms,  an  ice-making  capacity 
considerably  greater  than  the  weight  of  goods  to  be  frozen 
per  hour  is  necessary.  The  heat  capacity  of  fish  is  roughly 
.8  as  much  as  that  of  water  in  both  the  solid  and  the  liquid 
state.  Therefore,  to  cool  fish  from  +75°  F.  to  + 10°  F.  would 
require  approximately  (75-32)X.8+.8Xl44-f  22X.4  =  148 
B.T.U.  Practically,  this  figure  is  only  a  rough  approxima- 
tion, because  it  is  usual  to  glaze  fish  in  a  coating  of  ice,  and 
this  adds  to  the  weight  to  be  frozen.  If  200  B.T.U.  are 
required  per  pound  of  fish,  the  equivalent  ice-making 

capacity  required  is  T7T  =  l-39  Ibs.  of  ice;   that  is,  a  plant 

which  would  handle  under  the  abovf  conditions  5  tons 
of  fish  per  hour  would  under  theoretically  ideal  conditions 
freeze  about  6.95  tons  of  ice. 

To  keep  theaters  and  auditoriums  cool  in  tropical  coun- 
tries and  even  in  New  York  City,  refrigerating  plants  have 
been  installed.  Such  a  plant,  just  as  in  the  case  of  a  sharp 
freezer,  would  be  rated  in  terms  of  its  ice-making  capacity, 
even  though  no  ice  is  made  for  use  as  ice,  Incidentally, 
there  is  some  ice  made  and  several  other  functions  per- 


256  HEAT 

formed  by  a  plant  of  this  character.     Actually  some  mois- 
ture is  frozen  out  of  the  air. 

The  bacteria  and  particles  of  putrefied  matter  are  usually 
taken  out  by  washing  the  air,  thus  keeping  it  free  from  odor. 
The  air  is  changed  often  enough  to  allow  each  person  at 
least  300  cu.ft.  per  hour.  A  person  at  rest  gives  off  about 
400  B.T.U.  and  there  must  be  air  enough  removed  to  take 
this  much  heat  away  if  the  room  temperature  does  not  rise. 

Problem  1.  If  100  Ibs.  of  ammonia  are  circulated  through  the 
plant  shown  in  Fig.  63,  what  is  the  temperature  of  the  gas  as  it 
enters  the  compressor  if  its  temperature  as  it  leaves  the  vat  is  15°? 

Problem  2.  With  conditions  as  in  Prob.  1.  what  must  have  been 
the  temperature  of  the  liquid  as  it  entered  the  evaporator? 

Problem  3.  If  the  temperature  of  the  ammonia  drawn  into 
the  cylinder  of  the  compressor  was  60°  F.,  what  would  have  been 
the  temperature  under  adiabatic  conditions,  if  compressed  from 
28-lb.  gauge  to  175-lb.  gauge? 

Problem  4.  If  the  weight  of  ammonia  passing  through  the 
compressor  in  Fig.  63  was  85  Ibs.,  what  must  have  been  the  tem- 
perature of  the  gas  as  it  left  the  compressor? 

Problem  5.  What  must  have  been  the  temperature  of  the 
ammonia  in  Prob.  4  after  it  had  passed  through  the  condenser? 

Problem  6.  How  much  work  must  the  compressor  have  done 
upon  the  gas  under  the  conditions  expressed  in  Prob.  3? 

87.  The  Absorption  Refrigeration  Plant.  The  absorp- 
tion system  of  refrigeration  is  like  the  compressor  system 
in  that  the  condenser  and  the  evaporator,  or  cooler,  are 
common  to  both,  and  perform  the  same  duty  under  almost 
the  same  conditions  in  both  cases.  The  absorption  plant 
differs  from  the  compressor  plant  in  that  the  function  of 
the  compressor  of  the  latter  is  performed  by  two  or  more 
parts  in  the  absorption  plant. 

The  compressor  may  be  considered  to  be  primarily 
engaged  in  sucking  out  the  ammonia  from  the  evaporator 
in  order  that  the  boiling-point  of  the  ammonia  in  the  evap- 
orator may  be  kept  low.  This  task  of  keeping  the  evap- 
orator or  cooler  free  from  ammonia  is  done  by  an  absorber 


X.     FUNCTION  OF  THE  REFRIGERATOR  PLANT     257 

in  the  absorption  plant.  Its  action  depends  upon  the 
property  of  ammonia  which  causes  ammonia  to  dissolve 
in  cold  water  in  large  quantities.  A  ratio  of  1000  volumes 
of  ammonia  to  1  of  water  is  possible. 

In  an  absorption  refrigeration  plant,  a  second  piece 
of  equipment  is  necessary  in  which  the  solution  of  ammonia 
pumped  from  the  absorber  may  be  heated  and  the  ammonia 
again  driven  off  under  high  pressure.  This  piece  is  called 
a  generator  and  is  simply  a  tank  heated  by  a  steam  coil 
placed  inside  of  the  tank.  A  pressure  can  be  maintained 
upon  this  coil  in  just  the  same  way  as  in  a  steam  boiler. 

88.  Cryogens.  The  name  by  which  FREEZING  MIXTURES 
are  technically  known  is  cryogens.  We  are  all  accustomed 
to  use  common  salt  (NaCl)  and  ice  to  cool  iced  food,  and 
confections.  The  action  depends  upon  the  fact  that  the 
freezing-point  of  a  solution  of  salt  in  water  is  very  much 
lower  than  that  of  either  the  pure  water  or  the  salt.  The 
solid  salt  mixed  with  solid  ice,  both  being  at  a  temperature 
well  below  32°  F.,  produces  a  liquid  solution  of  the  ice  and 
salt.  A  mixture  of  3  parts  by  weight  of  snow  at  32°  F. 
and  1  part  of  common  salt  at  32°  F.  if  placed  in  an  insulated 
calorimeter  will  rapidly  melt  into  a  mush  with  a  resulting 
temperature  of  —4.5°  F.  This  is  the  freezing-point  of  the 
salt  solution. 

This  is  by  no  means  the  lowest  temperature  which  can 
be  obtained  by  freezing  mixtures.  A  calcium  chloride  solu- 
tion (CaCk)  is  used  for  brine  in  some  cold  storage  plants 
because  it  is  reasonably  cheap  and  has  a  much  lower  freez- 
ing-point than  common  salt  (NaCl)  solution. 

If  we  mix  7  parts  of  snow  at  32°  F.  with  10  parts  of  crys- 
talline calcium  chloride  (CaCl2+6H2O)  the  temperature 
will  drop  to  -66.8°  F. 

NaCl  will  continue  to  be  used  in  freezing  mixtures  in 
place  of  the  more  expensive  salts  which  produce  the  lower 
temperature  because  the  quantity  of  energy  which  may  be 
absorbed  by  outside  bodies  is  not  in  proportion  to  the  reduc- 


258  HEAT 

tion  in  temperature  produced  by  the  cryogen.  In  many 
cases  the  more  snow  used  per  pound  of  salt  the  greater 
is  the  amount  of  energy  released  per  pound  of  salt  and  per 
pound  of  mixture. 

89.  The  Production  of  Low  Temperatures  by  Mechanical 
Means.  The  refrigerating  plants  discussed  in  the  previous 
sections  are  adapted  to  maintaining  temperatures  as  low  as 
10°  or  15°  F.  When  lower  temperatures  are  required 
it  is  necessary  to  use  a  different  gas  than  ammonia  for  the 
working  medium.  With  air-refrigerating  plants  it  is  pos- 
sible to  reduce  the  temperature  many  degrees  below  zero, 
the  plant  being  arranged  in  the  same  general  way  as  that 
shown  in  Fig.  62.  Such  plants  have  rather  small  com- 
merical  application  and  they  do  not  recommend  themselves 
to  scientific  research. 

The  study  of  extremely  low  temperatures  which  has 
resulted  in  the  production  of  liquid  air,  liquid  hydrogen, 
liquid  helium,  and  other  rare  gases,  has  only  been  possible 
with  a  modified  type  of  equipment.  Fig.  64  shows  a  lecture- 
room  equipment  for  making  liquid  air  which  illustrates 
many  of  the  principles  involved  in  low-temperature  work. 
A  tank  or  other  source  of  supply  for  air  or  other  gas  under 
a  high  pressure  is  necessary.  This  gas  is  led  through  a 
precooling  coil  in  DI. 

Z>i  contains  a  supply  of  cracked  ice  or  snow  and  is 
intended  to  cool  the  air  to  approximately  the  freezing- 
point  of  water.  The  air  may  next  be  led  through  Z>2,  which 
may  contain  a  freezing  mixture  capable  of  cooling  the  air 
to  —20°  or  —30°  F.  The  air  is  then  led  into  D3,  which  is 
a  carefully  insulated  chamber.  The  air  travels  downward, 
still  under  high  pressure,  through  the  coils  of  copper  tubing 
to  a  needle  valve  at  the  bottom.  This  valve  may  be 
adjusted  from  the  outside  by  turning  the  knob  F. 

In  this  apparatus,  just  as  in  the  refrigerating  plant,  the 
working  medium  under  pressure  and  previously  cooled  is 
allowed  to  expand  at  a  valve.  During  adiabatic  compres- 


X.     FUNCTION  OF  THE  REFRIGERATOR  PLANT    259 

sion  a  large  amount  of  heat  is  taken  out.  The  gas 
expands  when  it  comes  through  the  valve  to  atmospheric 
pressure,  does  work  against  the  atmosphere,  and  takes  the 
necessary  energy  from  itself.  Thus  the  gas  is  further  cooled. 
This  cold  gas  rises  and  comes  in  contact  with  the  copper 
tubing  which  supplies  air  to  the  valve.  The  tubing  and 


FIG.  64. — Air  Liquefier. 

the  compressed  gas  in  it  are  cooled  by  the  gas  as  it  rises  to 
escape  toward  E.  The  next  gas  to  reach  the  valve  will 
arrive  somewhat  cooler,  therefore,  and,  after  doing  work 
against  the  atmosphere,  will  expand  and  be  at  a  lower 
temperature  than  the  first  gas  to  pass  the  valve.  This 
colder  gas  will  in  turn  be  forced  upward  over  the  coils  and 
will  further  cool  them.  This  continual  cooling  of  the 


260  HEAT 

gas  in  the  pipe  goes  on  until  the  gas  that  comes  from  the 
valve  expands  and  cools  to  a  temperature  at  which  the  gas 
becomes  a  liquid.  Then  a  part  of  the  gas  is  liquefied  and 
collects  in  the  bottom  of  the  chamber  and  only  a  part 
returns  upward  over  the  pipes  to  keep  them  cold.  When 
this  condition  of  equilibrium  is  reached,  liquid  continues  to 
accumulate  in  the  bottom  of  the  vessel  so  long  as  the  supply 
of  gas  under  pressure  is  maintained. 

The  arrangement  of  coils  shown  in  Z>3  is  the  essential 
feature  of  what  is  known  as  the  REGENERATIVE  METHOD. 
The  student  will  see  that  this  is  simply  an  application  to 
the  problem  of  low  temperatures  of  the  countercurrent 
principle,  which  has  already  been  observed  in  distillation,  in 
the  steam  boiler,  and  in  condensers  generally.  By  having  the 
coil  in  Z)s  sufficiently  long  the  air  which  comes  out  at  E 
may  be  made  to  give  up  its  store  of  cold  so  completely  as 
to  be  warmed  to  practically  the  same  temperature  as  the 
gas  in  M . 

DI  and  Z>2  are  not  absolutely  essential  to  the  produc- 
tion of  even  such  low  temperatures  as  are  required  to 
liquefy  air,  but  they  greatly  increase  the  efficiency  of  the 
process.  If  hydrogen  is  to  be  made  in  DB,  it  is  practically 
necessary  to  put  liquid  air  in  Z>2  to  cool  the  supply  of 
hydrogen  which  will  flow  through  B,  C  and  M. 

Many  attempts  have  been  made  to  replace  the  needle 
valve  with  an  engine  or  turbine  which  would  use  the  gas 
adiabatically  to  do  external  work  in  addition  to  that  required 
to  expand  it  against  atmospheric  pressure.  If  adiabatic 
expansion  could  be  obtained  in  this  way,  a  much  greater 
quantity  of  liquid  air  per  pound  of  air  circulated  could  be 
obtained.  It  has  been  successfully  demonstrated  that 
this  may  be  done,  but  such  an  arrangement  has  not  come 
into  common  use. 

The  pressure  used  in  commercial  liquid  air  machines 
should  be  between  2500  and  3000  pounds  per  square  inch. 
To  compress  the  air  to  such  pressures  is  impossible  in  a 


X.  FUNCTION  OF  THE  REFRIGERATOR  PLANT  261 

single  stage.  Two,  three-,  or  four-stage  compressors  are 
therefore  used.  The  air  travels  from  the  first  stage  through 
water-cooled  coils  in  what  is  called  an  intercooler  to  the 
second  and  smaller  cylinder.  After  being  further  com- 
pressed in  the  second  cylinder  it  goes  through  a  second 
set  of  water-cooled  pipes  in  the  intercooler.  It  then  goes 
to  the  third  cylinder,  which  is  still  smaller  than  the  second. 
Between  the  third  and  fourth  cylinder  (if  a  four-cylinder 
compressor  is  used)  the  air  is  again  passed  through  the 
inter-cooler.  After  leaving  the  fourth  and  smallest  cylinder 
the  air  must  be  treated  in  a  tank  or  bomb  to  take  out  all 
moisture  and  CO2.  It  is  then  ready  to  be  passed  through 
a  pre-cooler  and  into  the  liquefier.  The  CC>2  is  usually 
taken  out  by  caustic  potash  and  the  water  by  caustic  soda, 
calcium  chloride,  or  other  suitable  compound.  Consid- 
erably over  a  quart  of  liquid  air  per  H.P.  hour  of  work 
done  may  be  obtained  in  a  modern  liquefier  of  the 
regenerator  type. 

Problem  7.  Assuming  that  Boyle's  law,  Charles'  law,  and  the 
law  for  adiabatic  expansion  all  apply,  how  much  work  would  be 
done  by  a  pound  of  air  against  the  atmosphere  if  it  expanded  from 
3000  Ibs.  per  square  inch  to  15  Ibs.  absolute?  Assume  also  that  the 
temperature  before  its  expansion  takes  place  was  -180°  C.  and 
as  it  escapes  from  the  apparatus  in  Fig.  65  at  E  it  was  at  —5°  C. 


The  volume  of  air  at  3000  Ibs.  pressure  (F2)  at  a  temperature 
of  -180°  C.  would  equal 

14.7X12.39    3000  V^ 
273  93     ; 

F2=.0207cu.ft. 

F3  =the  volume  of  air  at  —5°  C.  and  15  Ibs.  would  be 
14.7x12.39     15F3 
273        "  268  ' 
F3  =  11.92cu.ft. 


262  HEAT 

The  work  done  against  the  back  pressure  at  the  valve  will  be 
(Vz  —  Vz)  in  cubic  feet  X pressure  in  Ibs.  per  square  foot  or 
11.90X15X144=2570  ft.-lbs.;  this  equals  3.3  B.T.U. 

Problem  8.  If  air  is  admitted  to  an  apparatus  similar  to  that 
shown  in  Fig.  65  at  a  temperature  of  +5°  C.  in  the  pipe  M 
and  leaves  the  pipe  E  at  —  5°  C.,  what  weight  of  the  air  admitted 
in  Prob.  7  would  be  liquefied?  Assume  a  specific  heat  of  .17 
in  both  cases  and  the  latent  heat  as  51. 

Problem  9.  If  1  Ib.  of  air  passed  through  the  tube  M  in  Fig.  65 
at  a  temperature  of  20°  F.,  came  out  at  E  at  a  temperature  of  16°  F., 
and  no  liquid  was  formed,  how  many  B.T.U.  must  have  been 
extracted  from  the  coil  and  radiated  into  the  interior  of  D3? 

Problem  10.  What  would  be  the  total  work  required  to  com- 
press 1  Ib.  of  air  from  70°  adiabatically  to  3000  Ibs.  pressure  by  the 
following  stages : 

First      stage    75  Ibs.  and  pre-cooled  to  60°. 
Second     "250  "  li  60°. 

Third       "750  "  "  60°. 

Problem  11.  If  a  producer  gas  power  plant  with  an  efficiency 
of  20  per  cent  and  a  compressor  of  90  per  cent  efficiency  supply  air 
to  a  liquefier  which  delivers  1  qt.  of  liquid  air  per  horse-power  hour, 
what  weight  of  air  is  passed  through  the  liquefier  per  horse-power 
hour?  Assume  the  same  amount  of  work  done  per  pound  as  in 
the  previous  problem. 

Problem  12.  If  in  the  previous  problem  the  coal  for  the  gas 
producer  contains  14,000  B.T.U.  per  pound,  how  much  liquid  air 
per  pound  of  coal  was  produced? 

90.  Insulation  of  Cold-storage  Spaces.,  The  secret  of 
maintaining  a  low  temperature  lies  in  the  means  of  insulating 
which  are  adopted.  The  use  of  insulating  materials  has 
already  been  referred  to  in  the  last  chapter.  It  should 
be  pointed  out  in  this  connection  that  every  B.T.U. 
admitted  to  the  cold  space  in  a  store  room  or  in  a 
piece  of  low-temperature  apparatus  must  be  taken  out 
by  the  refrigerating  machinery  or  by  the  melting  ice  or 
cryogen  used. 

The  Dewar  bulb  shown  in  Fig.  61  illustrates  a  number 
of  points  in  design  which  are  worthy  of  attention. 


X.     FUNCTION  OF  THE  REFRIGERATOR  PLANT     263 

First:  It  will  be  noticed  that  the  only  opening  is  at 
the  top.  The  cold  gases  which  are  given  off  from  the  liquid 
contained  in  the  bulb  are  usually  more  dense  than  the 
warm  air  outside  and  consequently  do  not  promote  con- 
vection currents.  This  is  the  case  with  either  air,  oxygen, 
or  nitrogen. 

This  method  of  construction  has  sometimes  been  used 
to  advantage  in  building  cold  storage  rooms.  By  con- 
structing solid  walls  on  all  sides,  the  goods  may  be  taken 
in  on  the  top  floor  and  lowered  by  elevators  to  the  proper 
rooms.  Convection  currents  while  the  goods  are  being 
moved  are  thus  minimized,  and  only  the  heat  energy 
in  the  goods  themselves,  and  such  energy  as  is  conducted 
through  the  walls,  need  be  removed. 

Second :  Effective  insulation  requires  that  no  moisture  be 
conducted  inward  and  deposited  to  close  up  the  air  spaces 
in  the  fibrous  materials  used  as  insulation.  In  the  Dewar 
bulb  this  is  effectually  accomplished  by  the  vacuum.  In  con- 
structing refrigeration  store  rooms,  courses  of  tarred  paper 
are  laid  between  matched  boards,  and  brick,  or  cement 
walls  are  tarred  to  keep  moisture  from  going  inward  to 
the  cold  walls.  In  making  large  liquid-air  machines  the 
apparatus  corresponding  to  DS  of  Fig.  64  cannot  be  encased 
in  a  Dewar  bulb  as  shown  in  the  figure.  However,  the  plan 
adopted  by  Prof.  W.  P.  Bradley  of  Wesleyan  University,  who 
has  made  many  of  these  machines,  has  been  very  similar.  A 
double  case  of  tin  replaces  the  walls  of  glass  and  between 
these  is  packed  hair  felt.  If  the.  felt  is  thoroughly  dry 
when  introduced  and  the  tin  walls  are  then  carefully 
soldered  tight,  no  more  air  is  admitted  to  the  space  filled 
by  the  hair  felt,  and  therefore  no  moisture  can  be  con- 
veyed in. 

Third:  Radiation  is  prevented  by  placing  a  mirror 
surface  on  both  inner  walls.  The  outer  mirror  tends  to 
prevent  the  propagation  of  the  waves  by  the  outer  wall. 
The  inner  mirror  reflects  those  reaching  the  inner  surface. 


264  HEAT 

In  ordinary  refrigeration  the  radiation  losses  are  reduced 
to  a  minimum  by  using  opaque  materials  and  numerous  air 
spaces. 

The  pains  taken  in  any  commercial  installation  will 
depend  upon  the  cost  of  the  refrigeration  effect  required 
to  carry  away  the  excess  heat.  Any  investment  required 
to  improve  insulation  must  result  in  a  decreased  cost  of 
refrigeration  large  enough  to  make  the  investment  profit- 
able. 


X.     FUNCTION  OF  THE  REFRIGERATOR  PLANT     265 


REVIEW   PROBLEMS,   CHAPTER   X 

13.  A  small  refrigeration  plant  which  requires  100  H.P.  hours 
per  ton  of  ice,  is  operated  by  a  motor-driven  compressor.    The 
ammonia  enters  the  water-cooled  compressor  at  35°  F.  and  leaves 
it  at  145°  F.     It  enters  the  condenser  without  further  change  of 
temperature  and  leaves  as  a  liquid  at  180  Ibs.  absolute  pressure 
and  65°  F.    Without  further  change  in  temperature  it  entered 
the  evaporator  and  dropped  in  pressure  to  30  Ibs.  absolute  pressure. 
The  ammonia  gas  left  the  evaporator  (freezing  vat  or  congealer) 
at  25°  F.    80,000  B.T.U.  were  lost  from  evaporator  by  radiation, 
conduction,  and  convection.    Water  was  introduced  into  the  cans 
at  60°  F.  and  ice  was  withdrawn  at  a  mean  temperature  of  24°  F. 
The  latent  heat  of  ammonia  under  30  Ibs.  abs.  pressure  =556  B.T.U. 

180  Ibs.  abs.  pressure  =449  B.T.U. 

The  boiling-point  under    30  Ibs.  absolute  pressure  =  0°  F. 
180  Ibs.  absolute  pressure  =  89°  F. 
Compute  the  following  quantities  in  order: 
(a)  Heat  taken  out  of  the  evaporator  per  pound  of  ammonia 
circulated. 

(6)  Heat  given  up  per  pound  of  ice  made. 

(c)  Total  heat  to  be  taken  away  per  ton  of  ice  made. 

(d)  Total  weight  of  ammonia  which  must  have  been  circulated. 

(e)  Heat  radiated,  etc.,  from  piping  between  evaporator  and 
compressor. 

(/)  Total  energy  carried  away  by  the  circulating  water  of  the 
compressor  jacket.  (Assume  no  significant  quantity  of  heat  to  be 
radiated  or  otherwise  carried  from  the  compressor  except  by  the 
ammonia  gas  and  the  jacket  water.) 

(g)  Compute  the  energy  carried  from  the  condenser  by  the 
circulating  water.  (Assume  no  heat  lost  or  gained  except  in  the 
ammonia  gas  and  the  circulating  water.) 

(h)  Finally,  draw  the  energy  diagram  for  this  plant,  placing 
upon  it  all  of  the  results  computed  above  and  any  other  needed 
information. 

14.  Compute  the  useful  work  done  in  Prob.  13  by  the  com- 
pressor if  700  Ibs.  of  ammonia  per  ton  of  ice  had  been  circulated. 

15.  What  would  have  been  the  compressor  efficiency  in  Prob.  14? 


266  HEAT 

16.  How  much  water  could  have  been  frozen  in  Prob.  13  if 
the  water  had  been  taken  in  at  32°  F.,  and  the  ice  delivered  at 
32°  F.? 

17.  Assuming  that  the  laws  for  perfect  gases  apply,  how  much 
work  would  be  done  by  a  pound  of  hydrogen  expanding  adiabat- 
ically  from  3000  Ibs.  to  15  Ibs.  absolute  pressure  in  apparatus 
similar  to  that  shown  in  Fig.  65?    Temperature  at  the  valve  before 
expansion  257°  C.    Temperature  at  E  5°  C.  above  that  at  D. 

18.  In  Prob.  17  the  temperature  of  the  hydrogen  in  M  was 
—  180°  F.    Assuming  that  the  specific  heat  is  as  given  in  the  table, 
find  the  weight  of  liquid  formed. 


X.     FUNCTION  OF  THE  REFRIGERATOR  PLANT     267 


SUMMARY,   CHAPTER  X 

The  problem  of  refrigeration  consists  first  in  removing 
heat,  and,  second,  in  keeping  it  out. 

The  LATENT  HEAT  OF  FUSION  of  ice  is  the  chief 
source  of  cold  in  refrigeration.  Ice  by  melting  absorbs  heat 
and  takes  it  from  the  cold  storage  space  when  the 
water  flows  away. 

In  the  MECHANICAL  REFRIGERATING  PLANT 
liquid  ammonia  or  other  suitable  substance  is  made  to 
evaporate  in  the  piping  in  the  cold  room.  In  all 
the  common  commercial  machines  the  latent  heat 
of  vaporization  takes  up  the  heat  and  the  gas  formed 
takes  away  the  heat  of  vaporization  plus  some 
sensible  heat. 

By  insulation,  the  heat  conducted,  conveyed,  and 
radiated  in  may  be  greatly  reduced. 

The  plant  must  take  away  all  of  the  heat  brought  in 
with  the  articles  to  be  refrigerated. 

CRYOGENS,  or  freezing  mixtures,  are  usually  mix- 
tures of  two  solids  which  melt  into  a  solution  of  much 
lower  freezing-point  than  that  of  either  solid  alone. 
The  source  of  refrigerating  effect  is  then*  latent  heat  of 
fusion. 

LOW  TEMPERATURES  are  obtained  in  practice 
by  expanding  a  gas  at  a  valve  in  an  apparatus  which 
keeps  out  the  heat  energy  by  using  the  counter- 
current  or  regenerative  principle. 


CHAPTER  XI 
INSTRUMENTS 

91.  Instruments  for  the  Measurement  of  Temperature. 
To  measure  temperature  we  usually  employ  an  instrument 
known  as  a  thermometer  or  a  pyrometer.  The  action  of 
these  instruments  depends  upon  some  effect  which  accom- 
panies a  change  of  temperature.  Illustrations  of  such 
effects  are:  the  expansion  of  a  solid,  liquid,  or  gas,  the 
change  in  resistance  of  an  electrical  conductor,  the  thermo- 
electric E.M.F.  in  a  thermo-j unction,  or  the  difference 
in  quantity  of  energy  radiated  because  of  the  change  in 
temperature. 

When  any  effect  is  taken  as  a  means  of  producing  a 
reading  in  the  instrument,  the  accuracy  of  the  readings  as 
indications  of  the  true  temperature  will  depend  upon  the 
uniformity  of  this  effect  with  relation  to  the  change  of 
temperature  unless  some  correction  is  automatically  made. 
There  are  no  effects  known  which  are  directly  in  proportion 
to  the  change  in  temperature.  Thus  the  expansion  of  a 
substance  is  never  uniform  over  any  considerable  range  of 
temperature.  At  some  temperatures  a  solid  may  even  con- 
tract with  increase  of  temperature.  Therefore,  either  the 
scale  of  the  instrument  must  be  constructed  in  a  way  to 
correct  for  the  irregularity  of  the  effect,  or  the  readings 
must  later  be  revised  to  correct  for  the  irregularity. 

The  linear  expansion  of  a  solid  with  an  increase  of 
temperature  is  often  taken  advantage  of  in  portable  ther- 
mometers and  thermostats.  Usually  these  instruments  con- 
tain a  rod  or  strap  made  of  two  thin  strips  of  different 

268 


XI.     INSTRUMENTS  269 

metals.  One  end  of  each  strip  is  fastened  to  a  rigid  frame. 
The  remaining  ends  are  fastened  together  and  to  the  record- 
ing mechanism.  The  two  metals  are  so  selected  that  there 
is  a  large  difference  between  their  rates  of  expansion.  Upon 
change  of  temperature,  one  therefore  becomes  longer  than 
the  other,  and  since  their  two  ends  are  fastened  together, 
the  one  expanding  the  more  bends  the  other  over  into  a 
crescent  shape.  The  end  attached  to  the  mechanism  is 
thus  made  to  move  and  to  drive  an  indicator  about  a  dial, 
in  the  case  of  a  thermometer,  or  to  close  an  electric  circuit 
or  open  a  valve,  in  the  case  of  a  thermostat. 

A  thermometer  constructed  in  this  way  may  be  arranged 
to  indicate  a  wide  range  of  temperatures.  The  readings  are 
only  approximate  indications  of  the  temperatures. 

For  scientific  purposes  a  thermometer  is  most  often 
used  over  a  short  range  of  temperature,  and  frequently 
it  is  not  so  important  to  know  just  what  the  temperature 
is  as  it  is  to  know  what  is  the  difference  in  temperature. 

For  accurate  determinations  of  differences  in  tem- 
perature the  amount  of  expansion  of  a  liquid  or  a  gas  is 
ordinarily  used.  In  cases  where  a  fluid  is  used,  either  the 
change  in  volume  or  the  change  in  pressure  of  the  fluid 
may  be  used  as  a  means  of  indicating  the  temperature 
change. 

In  the  most  common  types  of  thermometers,  liquids 
are  encased  in  a  bulb.  To  this  bulb  is  attached  a  long  stem 
and  the  change  in  volume  is  indicated  by  the  motion  of  a 
thread  of  the  liquid  up  or  down  the  stem.  Therefore,  to 
indicate  temperatures,  the  scale  must  be  graduated  so  that 
lengths  along  it  are  in  proportion  to  the  change  in  volume. 
The  length  between  any  two  marks,  indicating  two  different 
temperatures,  is  the  particular  length  of  bore  along 
the  tube  which  will  be  filled  by  the  liquid  expanding 
out  of  the  bulb  when  the  temperature  changes  from  the 
value  indicated  by  the  first  mark  to  the  value  indicated 
by  the  second  mark.  The  mercury  thermometer  and  the 


270  HEAT 

alcohol  thermometer  are  of  this  type  and  are  in  universal 
use. 

92.  Mercury  Thermometers.  Every  student  who  reads 
this  text  has  probably  seen  and  used  mercury  thermometers. 
The  only  new  things  which  he  needs  to  know  about  them 
are  related  either  to  their  construction  or  to  their  scientific 
and  technical  use. 

To  make  a  mercury  thermometer  the  first  step  is  to 
select  a  stem  of  uniform  bore.  Upon  this  is  fused  a 
cylindrical  bulb  of  a  capacity  to  correspond  with  the  range 
of  the  thermometer.  By  inserting  the  open  end  of  the  stem 
in  mercury  and  heating  the  bulb,  the  air  which  it  contains 
may  be  partially  driven  out,  and  upon  cooling,  the  mercury 
will  be  forced  in  by  atmospheric  pressure  to  replace  the 
air  driven  out.  By  inverting  the  bulb  and  heating  again, 
some  more  air  can  be  driven  out  and  the  space  thus 
emptied  filled  with  mercury.  By  repeating  this  process 
a  number  of  times  a  sufficient  quantity  of  mercury  may  be 
introduced  to  practically  fill  the  space.  The  thermometer 
is  then  heated  until  the  air  is  all  driven  out  and  the  mer- 
cury expands  sufficiently  to  fill  the  bulb  and  the  stem. 
The  top  is  then  sealed  off.  When  the  mercury  cools  a 
vacuum  is  left  above  the  mercury.  Then  the  thermometer 
is  laid  away  to  age  for  from  a  week  to  a  year,  depending  upon 
the  accuracy  of  the  instrument  desired. 

To  calibrate  this  instrument  two  so-called  "  fixed  points  " 
are  obtained.  One  is  the  freezing-point  of  water.  This 
point  is  marked  upon  the  thermometer  in  wax  pre- 
viously placed  upon  the  stem.  The  position  of  the  mark 
is  determined  by  placing  the  thermometer  in  a  mixture  of 
ice  and  water  and  allowing  the  mercury  to  come  to  rest. 

The  second  fixed  point  on  a  thermometer  is  the  boil- 
ing-point of  water  under  standard  conditions  of  pressure. 
This  point  is  marked  in  a  way  similar  to  the  first.  By 
enclosing  the  bulb  and  stem  in  steam  under  atmospheric 
pressure  the  position  of  mercury  corresponding  to  the  tern- 


XI.     INSTRUMENTS  271 

perature  of  boiling  water  may  be  located  by  a  scratch  in 
the  wax.  Graduations  are  then  etched  upon  the  glass  by 
applying  hydrofluoric  acid. 

On  page  13  it  is  stated  that  these  two  fixed  points  on 
the  Fahrenheit  scale  are  respectively  32°  and  212°.  On 
the  Centigrade  scale  they  are  at  0°  and  100°. 

In  cheap  thermometers  the  space  between  the  boiling- 
and  freezing-point  is  then  divided  into  equal  graduations, 
marked  according  to  the  system  used;  sometimes  a  uniformly 
graduated  paper  scale  is  attached  at  approximately  the 
correct  position.  Good  thermometers  usually  have  the 
scale  graduated  on  the  glass  stem,  according  to  the  sys- 
tem used.  If  a  thermometer  is  to  be  used  as  a  standard, 
the  divisions  between  the  freezing-point  and  the  boiling-point 
must  be  made  with  some  regard  to  the  inequalities  in  the  bore 
of  the  stem.  It  must  be  remembered  that  the  calibration 
should  properly  be  in  units  of  volume,  because  the  expansion 
of  mercury  is  a  volumetric  effect  and  not  a  linear  effect. 

To  find  these  inequalities  and  determine  the  value  of  the 
degree  spaces  at  each  portion  of  the  stem,  a  small  thread 
of  mercury  is  broken  from  the  main  thread  and  is  moved 
along  the  bore  by  short  intervals,  starting  from  one  of  the 
two  fixed  points.  By  the  use  of  a  microscope  the  length 
along  the  stem  occupied  by  the  thread  is  carefully  observed 
for  each  successive  position  of  the  thread.  By  careful  ma- 
nipulation this  short  thread  may  be  made  to  move  along 
the  whole  length  of  the  tube  step  by  step,  thus  measuring 
off  lengths  along  the  bore  which  will  contain  equal  volumes. 
These  lengths  are  then  subdivided  into  equal  parts.  The 
more  steps  taken  in  calibrating  a  given  length  the  greater 
the  accuracy.  In  this  way  errors  due  to  inequality  of 
bore  and  unequal  volumetric  expansion  can  be  avoided  at 
the  intermediate  points  along  the  scale. 

If  the  thermometer  is  to  be  calibrated  for  higher  tem- 
peratures than  212°  F.,  it  may  have  other  fixed  points 
determined,  such  as  the  melting-point  of  sulphur  or  certain 


272  HEAT 

salts.  Yellow  phosphorus  melts  at  43.3°  C.,  sulphur  melts 
at  approximately  115°  C. .  and  boils  at  441.7°  C.,  sodium 
chloride  melts  at  774°  C.,  etc. 

The  advantages  of  mercury  as  a  thermometric  liquid 
lie  in  the  facts  that  it  is  a  good  heat  conductor,  has  a  low 
specific  heat,  is  easily  seen  even  when  the  thread  is  very  fine, 
does  not  wet  the  tube,  does  not  cling  to  the  glass,  and  has 
a  practically  uniform  rate  of  expansion  between  0°  C.  and 
100°  C.  Its  use  is  limited  by  the  fact  that  it  freezes  at 
—38.2°  F.,  and  that  its  vapor  tension  is  excessive  for 
temperatures  above  1000°  F.  In  fact  if  it  is  to  be  used  for 
temperatures  above  400°  F.,  it  is  necessary  to  admit  nitrogen 
to  the  space  above  the  mercury,  before  sealing  off  the  stem,  to 
prevent  boiling  and  "  bumping  "  at  the  higher  temperatures. 

In  the  preliminary  report  of  the  power  test  committee, 
A.S.M.E.  Journal,  page  1696,  the  following  statements  are 
made  concerning  thermometers : 

"  Standard  thermometers  are  those  which  indicate  212°  F.  in  steam 
escaping  from  boiling  water  at  the  normal  barometric  pressure  of 
29.92  ins.  (referred  to  32°),  the  whole  stem  up  to  the  212°  point 
being  surrounded  by  the  steam;  and  which  indicate  32°  F.  in  melting 
ice,  the  stem  being  likewise  completely  immersed  to  the  32°  point; 
and  which  are  calibrated  for  points  between  and  beyond  these  two 
reference  marks.  For  temperatures  between  212°  and  400°  F.  the 
comparison  of  the  thermometer  should  be  made  with  the  temperature 
given  in  Marks  and  Davis'  Steam  Tables,  the  method  required  being  to 
place  it  in  a  thermometer-well  surrounded  by  saturated  steam  under 
sufficient  pressure  to  give  the  desired  temperature.  The  pressure 
should  be  determined  by  a  correct  gauge,  and  the  thermometer  should 
be  immersed  to  the  same  extent  as  it  is  under  its  working  condition. 

"A  thermometer-well  consists  of  a  hollow  plug  threaded  at  the 
upper  end  and  screwed  into  a  threaded  hole  in  the  top  of  a  horizontal 
pipe,  the  lower  part  extending  vertically  into  the  interior  of  the  pipe 
as  far,  if  practicable,  as  the  center.  The  inside  diameter  should  be 
slightly  larger  than  the  outside  diameter  of  the  thermometer  tube 
and  the  well  should  be  filled  with  soft  solder  for  higher  temperatures. 

"For  superheated  steam  the  immersed  portion  should  be  fluted  so 
as  to  increase  the  area  of  the  absorbing  surface. 

"Thermometers  are  so  readily  broken  that  it  is  desirable  in  impor- 


XI.     INSTRUMENTS  273 

tant  tests  to  have  a  sufficient  number  on  hand  that  in  case  of  accident 
the  readings  will  not  be  interrupted.  These  spare  thermometers 
should  preferably  be  calibrated." 


Every  accurate  mercury  thermometer  is  made  by  hand 
methods.  There  is  no  known  way  of  making  the  parts  by 
machinery,  as  bolts,  screws,  etc.,  can  be  made.  After  they 
are  made  with  care  their  value  also  depends  upon  the  care 
and  skill  with  which  they  are  calibrated  and  aged. 

The  raw  materials  in  a  ten-dollar  thermometer  cost, 
at  most,  only  a  few  cents.  The  difference  in  cost  of  high- 
grade  materials  and  of  cheap  materials  is  very  little.  Thus 
in  every  stage  in  the  making  of  mercury  thermometers, 
the  quality  of  the  product  and  the  cost  are  dependent  almost 
absolutely  upon  the  workmanship  used  upon  it. 

In  Bohemia,  girls  make  thermometers  in  large  quantities. 
These  are  frequently  so  cheap  that  they  may  be  had  for  a 
few  cents  a  dozen.  To  the  casual  observer  there  is  little 
difference  between  a  50-cent  thermometer  and  a  $5  ther- 
mometer. The  writer  has  recently  been  offered  thermometers 
at  35  cents  for  which  he  has  seen  others  pay  $2. 

Since  the  value  lies  in  the  workmanship  and  since  there 
is  no  easy  way  of  telling  at  a  glance  the  amount  of  skill  and 
labor  used  in  making  the  instrument,  the  problem  of  pur- 
chasing thermometers  is  a  difficult  one.  There  are  a  few 
reliable  makers  who  guarantee  each  of  their  thermometers 
and  do  all  in  their  power  to  keep  the  methods  of  making 
the  instruments  such  as  to  enable  them  to  exceed  their 
guarantee. 

The  detail  operations  in  the  art  of  making  thermometers 
may  be  varied  greatly.  Each  maker  guards  his  own  process 
as  a  trade  secret  and  will  not  explain  any  details  other  than 
those  which  are  of  advertising  value. 

There  is  a  maker  in  Brooklyn,  N.Y.,  who  has  an  excellent 
reputation  for  making  reliable  thermometers.  The  only 
point  which  he  will  give  out  for  publication  is  that  the  bulbs 


274  HEAT 

on  his  standard  thermometers  are  all  made  from  a   single 
pot  of  glass  made  for  him  in  Jena,  Germany,  in  1889. 

The  composition  of  this  glass  is  said  to  be  such  that 
it  ages  quickly  and  then  upon  repeated  expansion  it  always 
returns  approximately  to  the  original  condition.  The  glass 
contains  no  lead,  but  has  7  per  cent  of  oxide  of  zinc.  This 
maker  estimates  that  he  will  have  enough  glass  in  this  single 
pot  to  last  a  lifetime.  Another  advantage  in  using  the 
same  glass  for  all  the  bulbs  lies  in  the  fact  that  the  rate 
of  thermal  expansion  of  all  thermometers  of  this  make 
is  the  same,  and  after  the  thermometers  are  aged  they 
will  continue  to  check  one  against  the  other  for  an  indefinite 
length  of  time.  Since  practically  all  of  the  volume  of 
mercury  is  enclosed  in  the  bulb,  the  readings  of  the  ther- 
mometer are  almost  entirely  dependent  upon  the  expan- 
sion in  the  bulb.  For  this  reason  only  the  bulb  needs  to 
be  made  of  the  special  glass,  as  the  expansion  effects  in  the 
stem  have  no  significant  effect  upon  the  readings. 

93.  Alcohol  Thermometers.    Alcohol  thermometers  are 
used  chiefly  for  low  temperatures  where  there  is  danger 
of  the  mercury  freezing.     In  case  a  large  thermometer  for 
show  windows  or  for  outside  use  in  a  public  place  is  desired, 
alcohol  is  somewhat  more  convenient  because  it  has  a  larger 
coefficient  of  expansion,  and  therefore,  gives  a  larger  visible 
effect  for  the   same   quantity   of  liquid  used  in  the  bulb 
and  for  the  same  change   in  temperature.     It   is   always 
calibrated  against  a  mercury  standard  or  gas  standard  ther- 
mometer.    Turpentine,  pentane,  and  various  other  liquids 
are  also  occasionally  used  to  replace  the  mercury.     Alcohol 
thermometers   are   not   adapted   to   use   for   temperatures 
above  the  boiling-point  of  alcohol,  78°  C. 

94.  Sensitive   Thermometers.    By    making  the  bore  of 
the  stem  very  fine  as  compared  to  the  size  of  the  reservoir 
at  the  bottom,  it  is  possible  to  make  a  thermometer  which 
will    be    very    sensitive    to    small    changes    in     tempera- 
ture.      In    this    way  thermometers   are  constructed  which 


XI.     INSTRUMENTS  275 

read  differences  in  temperature  to  a  thousandth  of  a 
degree  F. 

To  avoid  making  the  stem  very  long,  a  large  bulb  is 
blown  at  the  top  of  the  stem  of  the  thermometer  and  part 
of  the  mercury  is  placed  in  the  upper  reservoir  when  the 
range  of  temperatures  is  higher  than  can  be  read  other- 
wise. In  this  event  only  differences  in  temperature  are 
indicated  correctly. 

95.  Gas  Thermometers.  Thermometers  used  for  ulti- 
mate standards  in  extremely  accurate  scientific  work  are 
of  the  gas  thermometer  type.  The  apparatus  used  is  sim- 
ilar in  principle  to  that  shown  in  Fig.  20.  When  extreme 
accuracy  is  desired,  however,  a  great  many  refinements  are 
added.  If  in  Exp.  H  1-3,  page  86,  we  assume  that  we  know 
the  rate  of  expansion  of  the  air  in  the  bulb,  A,  and  the 
rate  of  expansion  of  the  glass,  and  if  in  addition  we  know 
the  pressure  required  to  keep  the  mercury  at  M,  at  0°  C., 
we  will  be  able  to  determine  the  temperature  of  the  bulb, 
A,  under  any  other  set  of  conditions. 

In  writing  up  the  computations  on  page  88  the  data  marked  1  was 
not  used.  From  this  we  may  compute  the  true  room-temperature 
as  follows: 

/>"=41+2T4(°)  I 

where  t°  is  the  temperature  centigrade.     Substituting, 


274(1.26)  =  14.18  t°; 
i°=24.3. 

Now  this  result  does  not  work  out  to  agree  with  the  thermometer 
reading  taken  at  the  time.  The  difference  may  be  due  in  part  to  the 
fact  that  thus  far  no  correction  has  been  applied  to  this  first  reading 
for  the  expansion  of  the  mercury.  The  thermometer  used  for  the 
measurement  of  the  room  temperature  should  be  charged  with  the 
remainder  of  the  deviation  in  results. 


276  HEAT 

The  only  practical  limits  to  the  use  of  this  apparatus 
as  an  air  thermometer  are  the  melting-point  of  the  glass, 
the  temperature  at  which  the  air  is  liquefied,  and  the  point 
where  oxidation  of  the  glass  would  begin.  By  using  nitro- 
gen instead  of  air  and  by  using  procelain  or  quartz  in  place 
of  glass,  the  upper  limit  may  be  raised  many  hundred 
degrees. 

There  is  no  permanent  gas  whose  rate  of  expansion  is 
absolutely  uniform  and  in  direct  proportion  to  the  tem- 
perature over  a  wide  range.  The  factors  of  correction, 
however,  for  hydrogen  and  nitrogen  have  been  determined 
with  great  accuracy  and  the  hydrogen  thermometer  is  the 
standard  for  temperatures  below  200°  C.  and  the  nitrogen 
thermometer  for  temperatures  above  200°  C. 


FIG.  65, — Resistance  Pyrometer  Bulb. 

96.  Pyrometers.  There  are  two  common  types  of 
pyrometers  in  commercial  use  in  this  country :  the  resistance 
pyrometer  and  the  thermo-j  unction  pyrometer. 

The  types  will  be  well  enough  understood  from  the 
description  of  one  make  of  each  type  given  in  the  following 
paragraphs. 

Fig.  66  shows  the  arrangement  of  parts  in  the  Leeds 
&  Northrup  resistance  pyrometer.  This  instrument  con- 
sists essentially  of  two  parts.  First:  a  resistance  coil  of 
platinum  or  other  refractory  metal  protected  by  a  long 
tube  of  metal,  porcelain,  or  quartz.  This  is  called  the 
bulb.  Second:  a  modified  form  of  Wheatstone  bridge, 
which  measures  the  change  in  resistance  with  change  of 
temperature  and  consequently  indicates  the  change  of 
temperature.  The  box  in  Fig.  66  holds  a  galvanometer 
and  a  bridge  combined.  The  dial  is  in  the  rheostat  arm 


XI.     INSTRUMENTS 


277 


of  the  bridge.     The  resistance  is  so  adjusted  that  the  dial 
reads  direct  in  degrees  for  a  given  range  of  temperature. 

The  resistance  of  the  bulb  changes  with  the  temperature 
approximately  according  to  the  law  stated  on  p.  78, 


where  a  is  a  coefficient  which  depends  upon  the  nature  of 
the  metal  used,  but  which  is  fairly  constant  over  wide  ranges 
of  temperature  for  the  alloys  and  metals  used. 


FIG.  66. — Resistance  Pyrometer. 

The  real  purpose,  or  function,  of  the  Wheatstone  bridge 
is  to  get  the  resistance  of  the  bulb.  From  this  resistance 
the  change  in  resistance  may  be  obtained  from  the  above 
formula. 


278 


HEAT 


The  bridge  may  be  made  to  read  the  change  in  resistance 
directly  by  placing  in  series  with  the  rheostat  arm  a  resist- 
ance equal  to  that  of  the  bulb  at  the  lowest  temper- 
ature for  which  the  instrument  is  to  be  used.  Any 
increase  in  temperature  above  the  lowest,  or  standard,  in 
temperature  produces  an  increase  in  resistance.  The 


FIG.  67. — Recording  Resistance  Pyrometer. 

electrical  circuit  may  be  so  arranged  that  no  current  will 
flow  when  the  rheostat  arm  is  adjusted  so  as  to  have  the 
same  amount  of  resistance  as  was  added  to  the  bulb  because 
of  the  rise  in  temperature  of  the  bulb.  If,  instead  of  mark- 
ing the  resistances  on  the  rheostat  arm,  the  increase  in  tem- 
perature which  produces  the  resistance  is  marked,  the 
pyrometer  becomes  direct  reading. 


XI.     INSTRUMENTS  279 

A  potentiometer  may  be  used  with  the  fire  end,  or 
bulb,  in  place  of  the  balance  indicator.  With  the  poten- 
tiometer the  change  in  resistance  may  be  measured  with 
greater  accuracy  and  consequently  the  temperature  may 
be  determined  more  accurately. 

97.  The  Bolometer.  The  bolometer  is  in  reality  a  delicate  type  of 
resistance  pyrometer.  Two  resistance  members  are  constructed  exactly 
alike,  each  being  made  of  ten  or  more  strips  of  blackened  platinum  foil, 
1  cm.  long,  5  mm.  wide,  and  .002  mm.  thick.  One  set  is  arranged 
to  be  exposed  to  radiated  rays  if  desired,  and  is  placed  in  the  unknown 
arm  of  the  Wheatstone  bridge.  The  delicate  set  is  placed  in  series 
with  the  rheostat  arm  and  is  always  protected  from  the  radiated  rays 
which  are  being  investigated.  The  bridge  enables  the  investigators  to 
obtain  the  change  in  resistance. 

If  radiated  rays  be  allowed  to  fall  upon  the  blackened  platinum 
they  will  be  absorbed  and  will  tend  to  increase  the  temperature  and 
consequently  the  resistance  of  the  platinum  foil.  This  effect  is  rapid 
since  the  weight  of  the  foil  is  so  small  that  the  heat  capacity  of  the 
foil  is  extremely  minute.  Less  than  .00000001  calorie  has  been 
sufficient  to  give  an  appreciable  reading. 

It  is  by  this  instrument  that  the  distribution  of  heat  energy  in 
the  spectrum  may  be  investigated. 

98.  Thermo-junction  Pyrometers.  The  Bristol  pyrom- 
eter is  a  good  sample  of  commercial  instruments  of  the 
thermo -junction  type.  It  has  two  fire  ends,  one  encased  in 
an  iron  tube,  for  temperatures  up  to  2000°  F.,  and  a  second 
encased  in  a  quartz  tube  for  temperatures  up  to  2200°  F. 

The  fire  ends  consist  simply  of  two  heavy  wires  of 
different  alloys,  welded  together  at  the  ends  but  otherwise 
insulated  by  an  asbestos  cover.  Tfhe  other  ends  of  these 
two  wires  are  connected  through  suitable  leads  to  a  milli- 
voltmeter.  This  instrument  has  a  double  scale,  and  a  double 
set  of  connections  and  reads  directly  in  degrees  F.  on  either 
scale. 

The  action  of  the  instrument  is  dependent  upon  a  very 
peculiar  electrical  effect  of  which  temperature  measurement 
is  the  most  important  practical  application.  To  produce 


280  HEAT 

this  effect,  two  wires  of  any  two  different  metals  or  alloys, 
such  as  one  platinum  and  one  platinum-iridium  wire,  are 
welded  together.  The  other  ends  are  connected  to  amilli- 
voltmeter  or  galvanometer.  Upon  the  application  of  heat  to 
the  welded  point  or  junction  a  difference  in  E.M.F.  is  set 
up  and  consequently  an  electric  current  will  flow  through 
the  electric  circuit.  The  amount  of  electrical  pressure 
(E.M.F.)  is  usually  in  proportion  to  the  difference  in  tem- 
perature between  the  ends  at  the  junction  and  the  other 
two  ends  of  the  wires  forming  the  junction. 

The  Bristol  pyrometer  is  often  equipped  with  a 
mercury  compensator  which  reduces  the  resistance  of  the 
circuit  with  rise  of  temperature  of  the  cold  ends  so  that  no 
corrections  need  to  be  made  in  the  scale  readings.  The 


I 

Bi. 

^y 

A 

f  — 

Sb. 

t 

FIG.  68. 

readings  of  a  thermo-couple  indicate  differences  in  tempera- 
ture and  not  definite  temperatures,  except  as  a  bath  may  be 
used  to  keep  the  ends  of  the  couple  which  are  connected 
to  the  instrument  at  the  temperature  for  which  the 
instrument  was  calibrated.  By  the  use  of  a  compensator 
this  difference  is  always  indicated  in  reference  to  a  standard 
temperature.  Thus  the  scale  may  be  made  to  read  tempera- 
tures directly. 

For  high  temperatures  it  is  necessary  to  select  metals 
or  alloys  which  will  not  oxidize  or  melt.  This  requirement 
limits  the  use  of  the  thermo-j unction  pyrometer  to  tem- 
peratures below  2500°  F.  For  measurements  by  scientists 
of  temperatures  above  the  melting-point  of  steel,  the  couple 
has  usually  been  made  up  of  platinum  and  a  platinum  alloy. 


XI.     INSTRUMENTS 


281 


The  alloy  contains  either  10  per  cent  of  iridium  or  10  per 
cent  of  rhodium  and  90  per  cent  platinum.  In  the  Bristol 
pyrometer  various  alloys  are  used,  but  the  preferred  con- 
bination  for  instruments  used  in  tempering  steel  and  for 
other  high  temperature  purposes  is  tungsten  steel  and 
pure  nickel.  The  steel  is  positive  and  may  contain  from  5 
to  25  per  cent  of  tungsten.  The  nickel  is  negative  and 
may  be  alloyed  with  German  silver. 


FIG.  69. 

Uniformity  of  effect  is  usually  the  basis  of  selection  of 
the  thermo-j unction  for  low  temperatures.  Because  of  the 
small  heat  capacity  of  these  junctions  they  are  especially 
valuable  for  use  at  extremely  low  temperatures  such  as 
that  of  liquid  hydrogen. 

A  mil  li voltmeter  is  used  to  register  the  thermo-electric 
E.M.F.  produced  by  the  junction.  If  the  effect  is  in  direct 
proportion  to  the  E.M.F.,  the  difference  in  temperatures 
corresponding  to  linear  unit  deflection  may  be  marked  on  the 
scale  of  the  instrument.  By  the  use  of  a  compensator  or  a 
mercury  bath,  these  temperature  differences  become  direct 
readings  in  reference  to  a  standard  temperature. 


282 


HEAT 


A  potentiometer,  which  is  an  instrument  for  determin- 
ing E.M.F.,  may  be  used  with  a  thermo-j unction  when 
greater  accuracy  is  desired  than  can  be  obtained  with  a 
millivoltmeter. 


FIRE  END 


FURNACE  PATENTED 

SEPARABLE 
JUNCTION 


COLD  END  OF 
THERMO-ELECTRIC  COUP 


ATOR    M 


LEADS  TO  INDICATING  INSTRUMENT 


PATENTED  COMPENSAT 

FIG.  70. 

99.  Heat  Radiation  Pyrometers.  A  radiation  pyrometer  may  be 
constructed  by  connecting  a  large  number  of  thermo-junctions  in  series 
and  connecting  these  to  a  galvanometer.  The  large  number  of  junctions 
is  called  a  thermopile  and  multiplies  the  effect  of  a  single  couple  or 
junction.  For  a  given  change  in  temperature  the  E.M.F.  of  a  thermo- 
pile equals  the  E.M.F.  of  one  junction  times  the  number  of  junctions. 

One  or  more  of  these  junctions  may  be  mounted  upon  the  same 
suspension  which  supports  the  moving  coil  of  the  galvanometer  and 


be  connected  to  the  moving  coil.     In  this  way  the  parts  may  be  made 
extremely  light,  and  small  quantities  of  energy  may  be  made  to  produce 


XI.     INSTRUMENTS  283 

an  appreciable  deflection.  Radiations  are  allowed  to  enter  and  fall 
upon  the  junction  only.  Thus  the  junction  is  the  only  part  which  is 
heated. 

100.  Optical  Pyrometers.     Nearly  all  of    the  so-called    optical 
thermdhieters  compare  the  intensity  of  the  radiation  from  a  part  of 
the  spectrum,  such  as,  for  instance,  the  red  rays,  with  the  intensity 
of  illumination   from  a  standard  source.     In  other  words,   they  all 
compare  the    intensity  of  definite    wave    lengths.     A  photometer   is 
usually  used  for  the  comparison.      Optical  pyrometers  are  necessarily 
fragile  and  require  delicate  adjustments  and  a  large  amount  of  skill 
and  judgment  in  their  use.     Consequently,  they  are  not  adapted  for 
shop  work  in  the  hands  of  workmen. 

101.  Fuel  Calorimeters.     The  problem  of  obtaining  the 
heat  value  of  fuels  has  many  difficulties.     To  measure  the 
heat  produced  it  is  necessary  to  burn  a  small  sample  under 
conditions  that  will  produce  complete  combustion  and  will 
enable  the  investigator  to  measure  all  of  the  heat  [given  up 
during  the  burning. 

To  produce  complete  combustion  in  large  quantities  of 
coal  is  difficult  under  the  most  favorable  condition.  There 
is  usually  considerable  unburned  carbon  in  the  ash  and 
clinker.  To  completely  burn  a  sample  of  coal  or  oil  weigh- 
ing one  gram  and  to  measure  the  heat  accurately  is  very 
much  more  difficult.  All  blasts  which  would  tend  to  blow 
about  the  finely  divided  particles  of  fuel  as  sparks  must 
be  avoided.  A  high  temperature  must  be  maintained  both 
in  the  sample  and  in  the  flame,  because  complete  oxidation 
lakes  place  only  at  high  temperatures.  If  the  sample 
is  allowed  to  cool,  the  combustion  will  not  be  complete. 
If  the  flame  comes  in  contact  with  a  cold  wall,  combustion 
will  not  be  complete. 

Everyone  knows  that  a  single  large  lump  of  coal  removed 
from  the  fire  while  white  hot  soon  cools  and  stops  burning. 
A  small  quantity  of  powdered  coal  will  cool  almost  as  quickly 
if  exposed  in  a  similar  way.  On  the  other  hand,  if  a  live 
coal  is  held  in  oxygen  gas  it  will  be  seen  to  burn  brilliantly. 
This  gives  us  a  clue  to  the  two  methods  which  are  in  use 
in  commercial  determinations  of  the  fuel  value  of  a  coal. 


284 


HEAT 


First  Method.  In  Fig.  72  is  shown  a  so-called  Mahler 
bomb  calorimeter.  It  is  selected  as  a  typical  illustration 
chiefly  because  the  Mahler  design  was  the  first  moderately 
expensive  design  which  came  into  common  use  and  because 
it  is  still  in  use.  It  gets  its  name  from  the  heavy  walled 
"  bomb,"  B,  in  which  the  fuel  is  burned.  It  will  be  noticed 
that  the  walls  of  this  steel  bomb  are  thick  and  that  it  is 
provided  with  a  cover  which  may  be  screwed  on  tightly 
with  a  wrench  while  the  bomb  is  held  in  the  vise,  V.  The 


U/^ 


FIG.  72. — Mahler  Bomb  Calorimeter. 


weighed  sample  of  coal  is  placed  in  the  crucible,  C.  A  wire, 
F,  is  connected  to  the  rod,  E.  This  in  turn  passes  through 
an  insulating  bushing  and  makes  possible  an  electrical  con- 
nection to  the  outside.  The  other  end  of  F  makes  contact 
with  the  crucible,  if  it  is  nickel  or  platinum,  and  thus  the 
circuit  connection  is  made  to  the  metal  rod  holding  the 
crucible  and  to  the  bomb  itself.  To  pass  a  current  through 
the  platinum  coil,  F,  it  is  necessary  to  connect  one  wire 
from  a  source  of  electrical  energy  to  the  rod,  E,  and  a 


XI.     INSTRUMENTS  285 

second  wire  directly  to  the  bomb  itself.  When  a  current 
flows,  the  coil,  F,  can  be  heated  by  it  to  redness.  The  red- 
hot  platinum  wire  is  relied  upon  to  cause  the  fuel  to  ignite. 

To  make  a  determination,  one  gram  of  coal  is  placed 
in  the  crucible,  a  cover  (not  shown) ,  is  put  on,  and  the  wire, 
F,  is  adjusted.  A  known  weight  of  water  is  placed  in  the 
calorimeter  and  the  bomb  is  immersed  in  it.  Oxygen  is 
admitted  from  the  tank,  0,  until  the  gauge  pressure  is  about 
250  or  260  Ibs.  and  then  the  valve  is  closed.  The  stirrer,  S, 
which  carries  a  set  of  vanes,  is  made  to  rotate  by  moving 
the  screw,  K,  up  and  down  by  means  of  the  lever,  L.  The 
temperature  of  the  water  is  taken  with  the  thermometer,  T, 
and  the  electric  circuit  is  at  once  closed  to  ignite  the  coal,  S. 
The  thermometer  is  read  at  regular  intervals  until  several 
minutes  after  it  has  ceased  to  rise. 

From  the  rise  in  temperature,  the  weight  of  water  plus 
the  water  equivalent  of  the  calorimeter  and  bomb,  and  the 
weight  of  coal,  the  energy  per  pound  may  be  computed. 
The  value  will  be  what  is  often  called  the  higher  value. 
That  is,  it  will  be  the  value  which  results  from  cooling  all 
of  the  products  of  combustion  to  the  temperature  of  the 
apparatus.  To  do  this  will  result  in  the  condensation  of 
all  of  the  H2O  produced  in  the  form  of  steam  during  the 
combustion  of  any  constituents  of  the  coal  containing 
hydrogen.  The  value  which  does  not  include  the  latent 
heat  of  vaporization  of  this  condensed  water  is  called  the 
lower  value. 

This  apparatus,  like  all  bomb  calorimeters,  requires  a 
great  deal  of  skill  for  successful  operation.  Because  of  the 
high  pressures  necessary,  the  bomb  must  be  provided  with 
some  sort  of  lead  gasket  or  packing,  and  this  wears  out  very 
quickly. 

The  interior  of  the  bomb  is  usually  plated  with  platinum, 
gold,  nickel,  or  enamel  to  prevent  oxidization.  None  of 
these  coatings  is  durable  indefinitely,  although  platinum, 
with  care,  will  last  a  long  time. 


286  HEAT 

A  considerable  supply  of  oxygen  must  be  available  if 
a  number  of  determinations  are  to  be  made.  It  is 
estimated  that  the  present  minimum  cost  of  oxygen  for  the 
determination  of  the  fuel  value  of  1  gram  of  coal  in  an 
oxygen  bomb  is  10  cents. 

Second  Method.  There  are  many  makers  of  bomb  calorim- 
eters using  oxygen,  but  each  bomb  operates  in  practically 
the  same  way  as  the  Mahler  bomb  and  differs  only  in 
details  of  mechanical  construction.  It  is  possible  to  avoid 
the  use  of  oxygen,  however,  by  using  in  its  place  a 
chemical  compound  containing  oxygen.  Thus,  if  with  one 
gram  of  coal  there  is  mixed  3.25  grams  of  potassium 
nitrate  and  9.75  grams  of  potassium  chlorate,  complete  com- 
bustion may  be  obtained  without  an  external  supply  of 
oxygen.  This  mixture  might  be  placed  in  the  crucible, 
C,  of  Fig.  72  and  ignited  as  in  the  Mahler  bomb.  How- 
ever, it  is  usual,  whenever  this  method  is  followed,  to  use 
a  much  more  simplified  form  of  apparatus,  which  allows  the 
gaseous  products  to  bubble  up  through  water  and  then 
escape.  Results  obtained  tend  to  be  too  high  because  of 
the  heat  given  off  in  breaking  down  the  potassium  chlorate, 
and  they  tend  to  be  too  low  because  of  incomplete 
combustion. 

In  Fig.  73  is  shown  a  section  through  a  Bahrdt  calorim- 
eter and  an  enlarged  view  of  some  of  the  parts.  The  crucible, 
C,  is  used  to  contain  the  gram  sample  of  coal.  The  oxygen 
is  supplied  for  burning  this  through  the  pipe,  EA,  from  a 
cylinder  outside  of  the  apparatus.  Then  the  stopper  at  D 
supporting  the  crucible,  C,  is  placed  in  the  chamber,  P,  in 
the  left-hand  figure.  This  chamber  is  surrounded  by  a 
weighed  quantity  of  water  and  the  water  equivalent  of  the 
apparatus  is  determined  as  in  previous  experiments.  The 
fuel  may  be  ignited  by  first  placing  sulphur  on  top  of  it 
and  igniting  the  sulphur  with  a  hot  rod  before  placing  the 
crucible  in  the  chamber  or  it  may  be  ignited  electrically, 
as  in  the  Mahler  bomb.  The  products  of  combustion 


XI.      INSTRUMENTS 


287 


escape  through  the  spiral  copper  tubing  at  the  opening,  S, 
after  being  thoroughly  cooled  by  the  water.  The  results 
obtained  in  this  way  are  not  as  satisfactory  as  may 
be  obtained  from  a  bomb  calorimeter,  but  the  apparatus 
has  the  advantage  of  being  extremely  cheap  in  first  cost 
and  will  give  a  rough  comparative  test.  Liquids  may  be 
tested  in  the  same  apparatus  by  replacing  the  crucible,  C, 
and  the  stopper  at  D  with  a  lamp,  G,  placed  in  a  holder,  R, 
which  is  carried  by  the  stopper,  K.  The  weighed  amount 
of  fuel  is  placed  in  the  lamp,  G,  and  the  wick  is  ignited 


(Oxygon 


FIG.  73. — Bahrdt  Calorimeter  Parts. 

and  the  lamp  quickly  placed  inside  the  calorimeter.  The 
flame  is  watched  through  a  glass  plate,  0,  in  the  top  of 
the  chamber,  P,  of  the  left-hand  figure.  The  fuel  value 
of  any  distillate  which  does  not  leave  a  tarry  residue  may 
be  determined  in  this  way.  The  fuel  value  of  a  gas  may  be 
obtained  by  inserting  into  the  chamber,  P,  the  gas  burner, 
M,  which  extends  through  the  cork,  N.  To  use  this  appara- 
tus for  gas,  requires  a  gas  meter  to  measure  the  volume  of 
the  gas.  It  is  necessary  to  make  a  correction  in  the  readings 
of  the  meter  for  the  change  of  volume  from  that  under 
standard  conditions  due  to  the  temperature  and  the  pres- 
sure of  the  room. 


288 


HEAT 


102.  Steam  Indicators.  The  purpose  of  the  steam  indi- 
cator diagram  is  to  enable  the  steam  engineer  to  experi- 
mentally find  the  mean  effective  pressure  during  the  actual 
stroke  of  any  engine  or  compressor.  Whatever  the  special 
feature  or  design  added  by  the  maker,  the  indicator  must 
consist  primarily  of  a  small  cylinder  containing  a  piston 
which  moves  and  transmits  its  linear  motion  to  a  pencil. 
This  small  cylinder  connects  directly  with  the  main  cylinder; 
under  test,  therefore,  the  little  piston  is  made  to  move 
by  the  same  force  which  moves  the  big  piston.  The 


FIG.  74. — Thompson  &  Crosby  Indicator. 

piston  acts  against  a  spring  and  the  whole  device  must  be 
so  adjusted  that  the  motion  of  the  pencil  is  in  proportion 
to  the  gauge  pressure  of  the  steam.  The  range  of  the  instru- 
ment is  usually  varied  by  changing  the  spring.  Springs  are 
calibrated  in  terms  of  the  pressure  in  pounds  per  square  inch 
gauge  required  on  the  piston  to  produce  one  inch  motion 
of  the  pencil  and  usually  bear  this  number  stamped  upon 
them. 

Crosby   springs   are   designed    to    compress    an   amount 


XI.     INSTRUMENTS 


289 


equivalent  to  an  upward  motion  of  If  inches  and  they  act 
under  tension  for  pressures  less  than  atmospheric. 

All  makes  of  steam  indicators  have  a  rotating  drum 
which  carries  a  paper  "  card."  Upon  this  card  when  the 
drum  is  at  rest  the  pencil  may  be  made  to  trace  a  vertical 
line  by  the  motion  of  the  indicator  piston  caused  by  the 
pressure  in  the  engine  cylinder. 

If  the  lower  side  of  the  piston  is  connected  to  the 
atmosphere  the  piston  will  have  equal  pressures  on  both 


FIG.  75. — Section  of  Indicators. 

sides.  If  the  drum  is  rotated  it  will  then  trace  a  horizontal 
line  which  shows  the  atmospheric  pressure.  If  the  drum 
is  connected  through  suitable  cords  and  levers  to  the  cross- 
head  of  the  engine  it  may  be  made  to  move  with  the  piston 
in  the  cylinder  of  the  engine. 

When  the  piston  of  the  indicator  is  connected  to  one  end 
of  the  steam  cylinder  and  the  drum  is  rotated  from  the  cross- 
head,  these  motions  are  combined  and  a  figure  is  traced  on 


290  HEAT 

the  paper  like  that  shown  in  Fig.  64.  The  height  above 
the  atmospheric  line  at  any  point  indicates,  in  spring  units, 
the  pressure  on  the  piston  at  the  corresponding  point  in  the 
stroke.  By  determining  the  average  height  above  the 
atmospheric  line,  the  M.E.P.  (mean  effective  pressure)  for 
the  stroke  may  be  obtained. 

If  a  three-way  cock  is  used  in  piping  the  indicator  to 
the  ends  of  a  cylinder,  a  diagram  like  that  shown  in  Fig.  64 
may  be  obtained  by  connecting  the  piston  to  first  one  end 
and  then  the  other.  From  this  the  M.E.P.  for  each  end 
of  the  cylinder  may  be  obtained.  By  substituting  in  the 
formulae  in  Chapter  VI,  page  150,  the  I.H.P.  (indicated  horse- 
power) may  be  obtained. 

103.  Steam  Calorimeters.  To  determine  the  quantity  of 
heat  energy  in  a  given  weight  of  steam,  it  is  customary  to 
use  one  of  two  kinds  of  calorimeters;  either  the  throttling 
calorimeter  or  the  separating  calorimeter. 

The  Throttling  Calorimeter.  Where  the  quantity  of  the 
minute  drops  of  entrained  moisture  is  small,  the  throt- 
tling calorimeter  furnishes  the  most  accurate  means  of  finding 
out  the  per  cent  of  moisture  and  the  "  quality  "  of  the  steam. 
Fig.  76  shows  a  steam  calorimeter  of  the  throttling  type  made 
from  pipe  fittings.  This  consists  essentially  of  a  sampling 
tube  extending  into  the  steam  main  with  holes  arranged 
regularly  according  to  some  scheme  which  gives  a  fair  sample 
of  the  steam  passing  through  the  main.  Engineers  are  not 
agreed  as  to  the  best  method  of  obtaining  such  a  sample. 
The  journal  of  the  A.S.M.E.,  for  November,  1912,  page 
1836  and  context,  gives  a  description  of  the  calorimeter 
recommended  by  the  1912  code. 

The  steam  passes  the  thermometer  A  at  the  temperature 
and  pressure  of  the  steam  main.  It  next  passes  through  a 
f-inch  hole  in  a  small  disk  in  the  piping.  Here  it  expands 
to  atmospheric  pressure  without  any  loss  of  heat  energy. 
The  thermometer  B  reads  its  new  temperature.  It  may  not 
be  clear  to  the  student  at  first  that  the  temperature  of  the 


XI.     INSTRUMENTS 


291 


steam  should  be  different  when  it  reaches  thermometer  B 
from  that  at  A,  but  if  the  student  will  notice  in  the  steam 
table  the  temperature  of  saturated  steam  under  high  pres- 
sure such  as  165  Ibs.  will  be  373.2°.  At  atmospheric  pressure 
the  temperature  of  saturated  steam  is  212°.  Now,  if  the 
steam  in  the  steam  main  is  dry  and  saturated  it  will  contain 
1196.1  B.T.U.  of  heat  energy.  After  passing  through  the 
hole  in  the  disk  it  would  still  contain  this  1196.1  B.T.U. 
The  total  heat  of  dry  saturated  steam  at  14.7  Ibs.  pressure 


FIG.  76. — Throttling  Calorimeter. 

is  1150.1  B.T.U.  The  difference  between  these  two  total 
heats  or  46  B.T.U.  would  therefore  b,e  left  in  the  steam  and 
would  superheat  it.  The  amount  of  superheat  would  be 
46  divided  by  .48,  the  specific  heat  of  steam,  or  98°. 

If,  on  the  other  hand,  this  steam  had  contained  2  per  cent 
of  moisture  at  160  Ibs.  pressure,  there  would  have  been  2  per 
cent  of  the  water  which  would  not  have  had  any  latent 
heat  in  it,  but  only  the  sensible  heat  necessary  to  raise  it 
to  the  temperature  of  the  steam  at  this  pressure,  273.2°. 
This  2  per  cent  of  water  did  not  receive  latent  heat  energy 


292 


HEAT 


to  the  amount  of  .02X850.9,  or  17.02  B.T.U.  The  total 
heat  of  the  steam  containing  2  per  cent  of  moisture  was, 
therefore,  1179.1  B.T.U.  When  this  steam  was  expanded 
at  the  disk  to  atmospheric  pressure,  it  accordingly  had 
only  29.0  B.T.U.  in  it  which  caused  superheating.  The 
temperature  therefore  which  was  read  by  thermometer  B 
was  29.0  divided  by  .48,  or  60,4, 


Standard 
f  threads 


Plug 


FIG.  77. 

By  allowing  steam  of  unknown  quality  from  a  main  to 
blow  through  the  calorimeter  and  by  taking  the  reading 
of  the  thermometer,  the  problem  given  above  may  be  worked 
backwards  to  determine  the  quality. 

The  Separating  Calorimeter.  The  separating  calorimeter 
is  a  device  intended  to  mechanically  extract  the  entrained 
moisture  from  the  steam.  Thus  it  is  intended  to  take  out 
all  of  the  small  drops  of  water  and  deliver  dry  saturated 
steam. 


XI.     INSTRUMENTS  293 

The  inverted  cup  C  is  surrounded  with  gauze  or  other 
perforated  material.  The  steam  enters  the  area  above  the 
cup  and  then  passes  out  through  the  small  spaces  into 
the  central  space  B.  The  object  of  the  gauze  or  fine  per- 
foration is  to  provide  a  surface  upon  which  the  moisture 
may  collect  and  from  which  it  falls  in  large  drops  to  the 
bottom,  W.  The  dry  steam  rises  through  T,  T,  and  then 
passes  down  through  the  orifice,  0. 

The  water  in  W  rises  and  its  amount  may  be  directly 
read  upon  the  scale,  S,  by  observing  its  height  in  the  gauge 
glass,  G.  The  water  may  also  be  weighed  by  drawing  it 
off  through  the  cock  at  the  bottom  of  G. 

The  weight  of  dry  saturated  steam  passing  through 
the  orifice  may  be  computed  from  the  following  formula, 
which  is  frequently  used. 

The  quality  of  the  steam 


Wi+W2 

when  Wi  =  weight  of  the  steam  passing  through  the  orifice, 
0,  and  "PP2  =  the  weight  of  water  collected  in  W.  From  the 
quality,  the  total  heat  of  the  steam  may  be  readily  obtained 
from  the  steam  tables. 

The  separating  calorimeter  is  not  so  reliable  as  the 
throttling  calorimeter.  Therefore,  where  the  quantity  of 
moisture  in  the  steam  is  small,  the  throttling  calorimeter 
is  generally  used. 

Sometimes  a  throttling  calorimeter  is  connected  to  0 
on  the  separating  calorimeter.  In  .this  way  steam  having 
any  per  cent  of  moisture  may  be  accurately  tested  for 
moisture. 

Other  Calorimeters.  Various  schemes  have  been  used 
to  combine  the  effects  obtained  in  the  throttling  and  in  the 
separating  calorimeters.  The  student  should  have  no  trou- 
ble in  understanding  them,  however,  if  he  has  followed  the 
description  given  above  and  understands  the  throttling 
calorimeter. 


294  HEAT 

The  value  of  the  total  heat  of  steam  may  be  obtained 
by  condensing  it  in  a  barrel  of  cold  water  of  known  weight 
and  obtaining  the  rise  of  temperature  and  the  gain  in  weight 
of  the  water.  A  continuous-flow  condenser  may  also  be 
used.  This  consists  essentially  of  the  same  parts  as  the 
large  condenser  shown  on  page  168.  The  temperature  of 
water  is  measured  as  it  enters  and  leaves.  The  circulating 
water  and  the  condensed  water  is  weighed.  No  pump  is 
necessary  and  the  apparatus  may  be  rather  small. 

The  computation  is  similar  to  those  already  made  for 
the  condenser. 


APPENDIX   A 

TABLE  1 
USEFUL  NUMBERS 

22     circumference 

x  =  3.1416=~=  — •- .  Surface  of  cvl.  = 

7          diameter 

x2  =  9.8696;     -  =  .3183  =  ^-.  Volume  of  cyl.=xr2/. 

x  22 

Area  of  circle  =  xr2 = — -  =  .7854d2  =  —  d2.    Surface  of  sphere  =  4xr 2. 
4  14 

xd3     4*r« 
Volume  of  sphere = — = . 

£*  O 

6          3 

METRIC-ENGLISH  EQUIVALENTS 
-  cm.      =     .39  in.  1  in.      =     2.54    cms. 


1m.        =39.37  ins. 
m.        =  3.23  ft. 
km.      =     .6  mi. 
gm.      =     .035  oz.  (avoir.) 
kgm.    =  2.204  Ibs.  (avoir.) 
sq.cm.  =     .154  sq.in. 


ft.  =  30.48  cms. 
ft.  =  .305  m. 
mi.  =  1.60  km. 
oz.  =  28.35  gms. 
Ib.  =435.6  gms. 
sq.in.  =  6.45  sq.cms. 


cu.cm.  =     .061  cu.in.  1  cu.in.  =   16.39    cu.cms. 

1  litre     =     .2642  gal.  U.S.  1  gal.  U.S.  =3.785  litres. 

1  litre     =     .2200  gal.  British  1  gal.  British  =4.546  litres 

UNITS  OF  FORCE,   WORK,   POWER,   ETC. 
1  dyne  =  .00102  gm. 
lft.-lb.  =  1.356X107erga. 
1  joule  =  107  ergs. 
.    1  watt  =  107  ergs/sec.  =  1  joule/sec. 

MECHANICAL  EQUIVALENTS  OF  HEAT 
1  gm.  of  water  heated  1°  C.  =4.2  X107  ergs. 
1  Ib.  of  water  heated  1°  C.    =1400  ft.-lbs. 
1  Ib.  of  water  heated  1°  F.    =  778  ft.-lbs. 
780  ft.-lbs.  =  1  B.T.U. 
4.2X107gms.  =  l  calorie  (  =  4.2  joules). 
4.28  X104  gr.cms.  =  l  calorie  (  =  4.2  joules). 
4.2  watt'seconds  =  1  calorie  (=4.2  joules). 

(For  a  complete  table  showing  the  relation  between  the  variaus 
units  see  Table  II.) 

295 


296 


HEAT 


•g 

Is- 
IS  * 

m 

•c-§« 

«6s 

^0,'CM 


^  fts'gi 

1   -I! 

*iK<& 

"^£-§  QO'~Hc^ 
fe'JSfOcooocD'-i 
P  .J« )CO(N 

>o^ 


o.S 

IB 


^s^^-sg 

°o'^| 


es. 
. 


o 
o 
nits 
.m. 
oul 
-lbs. 
car 


.283  K.W.  h 
.379  H.-P.  h 
970  heat-u 
103,900  kjr. 
1,019,000  j 
751,300  ft.- 
.0664  Ib.  of 


<Nt 
C<l>-i 


•3.-  ». 
P-.S 


ilillll  L 


Z« 


^       O,  0  »-c  _, 

S 


M  <=>,. 


. 

53          <D 

C. 


^3  T3 
."S  c 
ft  «« 


£;ifl 


O<        C3CO< 

H     ^'< 


-*:l 


- 


S6i 


APPENDIX  A 


297 


TABLE  III 
HEAT   ENERGY    DEVELOPED    BY    OXIDATION 

(Assume  that  the  products  are  gaseous) 


GASES. 

B.T.U. 

Calories. 

Per.  Lb. 

PerCu.ft 

Per  Gm. 

PerCu.  Liter 

12,143 
3,040 
6,100 
16,700 
14,900 
3,090 

8,050 
1,800 
3,100 

Acetylene 

21,400 
20,400 
4,340 

13,600 
338 
680 
1,865 
1,677 
348 
1,500 
2,450 

11,930 
11,300 

2,440 

12,350 
11900 
34^60 

654 
1,541 
143 

7,180 
5,310 
6450 
9,980 
3,244 
1,150 
1,290 
10.400 
11,300 
11,003 
9,400 
12,200 

7,140 
2,420 
8,080 
321 
590 
730 
1,350 
9,200 
243 
6,080 
1,720 
14,544 
2,240 
575 
1,200 
4,420 
4,000 

Carbon  vapor 

Carbon  dioxide  to  COu 

Coal  gas  

Ethane  

22,200 
21,400 
62,030 

Ethylene  

Hydrogen 

Illuminants 

Nitrogen  to  NaO    

"          NO 

1  '          N2O5 

Pittsburgh  natural 

891 
200 
347 

Producer  (Siemens) 

Water  gas  (best) 

LIQUIDS. 
Alcohol,  ethvl  .    . 

12,900 

methyl  
denatured,  +8%  H2O  .  .  . 
Benzine 

9,540 
11,500 
17,900 
5,820 
20,700 



Carbon  disulphide 

Crude  oil,  sp.gr.  .886  
Dynamite  75% 

Fuel  oils,  sp.gr.  .965  
Gasoline,  sp.gr.  .720  
Kerosene,  sp.gr.  .795 

18,600 
20,300 
20,000 



Olive  oil  

Petroleum  ether,  sp.gr.  .689  
SOLIDS. 
Aluminium 

22,000 

Carbon  burned  to  CO 

14,544 
4,356 

CO2  
Copper  burned  to  Cu2O 

CuO  

Gunpowder 

Iron  burned  to  FeO 

Lard    

Lead  

Magnesium  

Manganese 

Naphthalene,  Ci0H8 

Sulphur       

Tin  

Zinc 

Wood  pine  +12.2%  H2O 

"      oak  +13.3%  H20  

298 


HEAT 


TABLE  IV* 
ANALYSIS  OF  VARIOUS  COALS 


^  I  Sample  No.  | 

Moisture. 

Volatile 
Matter. 

Fixed 
Carbon. 

4 

3 

Sulphur. 

Hydrogen. 

Carbon. 

2 

Oxygen. 

Calories  per 
Gramme. 

2.63 

33.00 

50.96 

13.41 

.94 

4.87 

70.73 

1.38 

8.67 

2 

3.36 

32.88 

51.33 

12.43 

1.01 

4.84 

68.69 

1.54 

11.49 

.... 

3 

3.24 

17.46 

66.69 

12.61 

1.24 

4.15 

74.09 

1.44 

6.47 

.... 

4 

2.23 

16.02 

72.55 

9.20 

1.87 

4.24 

78.83 

1.38 

4.48 

5 

2.19 

19.47 

66.71 

11.63 

1.28 

4.17 

75.31 

1.53 

6.08 

.... 

6 

38.81 

25.48 

27.29 

8.42 

.97 

7.09 

37.45 

.50 

45.57 

3526 

7 

33.38 

27.44 

29.62 

9.56 

.94 

6.77 

41.31 

.67 

40.75 

3994 

8 

22.71 

34.78 

36.60 

5.91 

.29 

6.14 

52.54 

1.03 

34.09 

5115 

9 

15.54 

33.03 

46.06 

5.37 

.58 

5.89 

60.08 

1.05 

27.03 

5865 

10 

11.44 

33.93 

43.92 

10.71 

4.94 

5.39 

60.06 

1.02 

17.88 

6088 

11 

3.42 

34.36 

58.83 

3.39 

.58 

5.25 

77.98 

1.29 

11.51 

7852 

12 

2.7 

14.5 

75.5 

7.3 

.99 

4.58 

80.65 

1.82 

4.66 

7845 

13 

3.26 

14.57 

78.20 

3.97 

.54 

4.76 

84.62 

1.02 

5.09 

8166 

14 

2.07 

9.81 

78.82 

9.30 

1.74 

3.62 

80.28 

1.47 

3.59 

7612 

15 

2.76 

2.48 

82.07 

12.69 

.54 

2.23 

79.22 

.68 

4.64 

6987 

16 

3.33 

3.27 

84.28 

9.12 

.60 

3.08 

81.35 

.79 

5.06 

7417 

*  From  U.  S.  G.  S.  Prof.  Paper  48.     Pages  196-200,  Smithsonian  Physical  Tables. 

TABLE  V 
GAS  ANALYSES   (BY.  VOLUME) 


No. 

CO2 

02 

CO 

H2 

CH* 

N 

C2H4 

H2S 

Ilium. 

1 
2 
3 

9.0 
.26 
80 

0.2 

.42 
1  8 

11.2 
.73 
3  5 

6.0 
1.86 
20  02 

8.9 
93.0 

72  18 

64.7 
3.02 
8  9 

.47 

.15 

6  30 

4 

1  16 

6  16 

50  59 

34  80 

2  06 

5  23 

5 

1  50 

50 

6.30 

50.10 

33.10 

2.70 

5.80 

6 

84 

25 

4  62 

43  95 

39  33 

4  79 

6  22 

7 

6  02 

30  28 

49  68 

3  46 

10  22 

0.34 

g 

6  10 

22  23 

28  7 

1  00 

41  9 

9 

12  9 

13  2 

24  8 

2  3 

46  8 

10 

17  4 

1  0 

1  0 

80  6 

11 

10.8 

8.4 

.30 

80.8 

NOTE.  1.  Producer  Gas,  U.  S.  G.  S.  Prof.  Paper  48,  Part  III,  p.  1136;  2. 
Natural  Gas,  E.  and  M.  Journal;  3.  Pittsburgh  Natural  Gas,  Poole;  4.  Newton, 
Mass.,  Coal  Gas  from  Poole  (Thwaite);  5,  6.  Paris,  France,  Coal  Gas  from  Poole 
(Thwaite);  7.  Bridgeport,  Conn.,  Water  Gas,  from  Poole;  8.  Producer  Gas, 
Siemens;  9.  Producer  Gas,  Mond's;  9,  10.  Flue  Gas,  B.  of  M.  Bui.  2,  p.  37. 


APPENDIX  A 


299 


TABLE  VI 
SPECIFIC  HEAT  TABLE 


Substance. 

Solid. 

Liquid. 

Gas. 

Range  in 
Temp. 
Deg.  C. 
From  To 

Spec. 
Heat. 

Range  In' 
Temp. 
Deg.  C. 
From  To 

Spec. 
Heat. 

flange  in 
Temp. 
Deg.  C. 
From  To 

Spec.  Heat. 

Const. 
P. 

Const. 
V. 

Air  

10,  100 
10,  100 

.238 
.508 

.055 

.216 
.242 
.147 

.487 
3.41 

.244 
.217 

.480 

.169 
.391 

.168 
.173 

2.81 

.173 
.155 

Alcohol,  ethyl  
'  '        methyl  

30 
5-10 

0 
19,38 

.615 
.590 

1.012 

.107 
.416 

Aluminium  

15,97 

.212 

Ammonia    

13,  106 

.0486 
.083 
.076 
.0298 
.094 
.084 

.242 
.204 
.105 

"        amorphous.  .  .  . 

9,102 
15,  100 

Bromine  

Benzine  

Carbon,  charcoal  
gas  coal  
diamond  
Carbon  dioxide  (CO2)  .  . 

8,98 
8,98 
8,98    - 

Carbon  monoxide  (CO) 
Chloroform  

.0933 

at  30 
at    0 

.235 
.529 

100,  120 
70,  200 

Copper  

15,  100 

Glass 

15,    97 

.12 
.20 

Hydrogen        .               .  . 

Iron,  cast    

.12 
.11 
.20 
0315 

.0402 
.0335 

"     wrought  

India-rubber  

Lead 

-70,  -40 
14,97 
100 

.0319 
.1092 
.113 

17,48 

Nickel 

Petroleum  
Platinum 

.0323 
.0559 
.117 
.180 

.056 
.033 
.034 

.  .  .  > 

16,20 
16,  20 

40 
20 

.460 

.332 

.576 

.459 
1.000 

100,  200 

Silver 

Steel      .... 

Sulphur  
Sulphuric  acid  
+5H2O 
Tin 

0-52 

Tantalum 

-185,  +20 
0,100 

Tungsten    

Turpentine  

Zinc  

0,100 
100 
200 
300 
-20,0 

.0935 
.095 
.100 
.104 
.504 

., 

,, 

Water  

300 


HEAT 


TABLE  VII 
COEFFICIENTS  OF  EXPANSION,   CENTIGRADE 


Substance. 

Linear.* 

xio* 

Substance. 

Cubical.  f 
X1Q3 

Aluminium  

2313 

SOLIDS 
Antimony 

3167 

/  Cast.  . 

.1875 

Bismuth  

4000 

Brass  <  „,. 
I  Wire. 

1930 

Ice 

1  1250 

Caoutchouc  

657- 

Iron    .        .  . 

3550 

.686 

Porcelain.  .  .    . 

1080 

f  Diamond  
Carbon    Gas  carbon  .... 
Graphite  

.0118 
.0540 
.0786 

Sulphur  

2.2373 

1  Anthracite  .... 
Copper.  . 

.2078 
1678 

LIQUIDS 

Ebonite  

.842 

A  ,    ,    ,  /  Ethyl 

1  042 

German  silver  

.1836 

Alcohols  ,,"•;,    ' 
I  Methyl. 

1  19 

(Tube  

0833 

Benzene 

1  18 

Plate  .  . 

.0891 

Ether  

1  52 

~ 

Crown  

.0897 

Glycerine  

49 

Flint  

0788 

Mercury 

182 

Ice 

51 

Olive  oil 

68 

Soft.. 

1210 

Petroleum 

90 

Cast  

1061 

Turpentine 

90 

Iron  j  Wrought  

.1140 

Steel 

1322 

Annealed.  .  .  . 

1095 

Lead 

2924 

Lead-tin  (solder)  
Magnesium  

.2508 
2694 

Nickel 

1012 

Paraffin  .  . 

1  0662 

Platinum  
Porcelain 

.0899 
0413 

Quartz  glass   . 

0026 

Silver  

1921 

Sulphur  

.6413 

Tin      . 

2234 

Wood,  parallel  to  fiber  : 
Oak  

.0492 

Pine  
Across  fiber,  Oak.  . 
Pine. 
Zinc.  . 

.0541 
.544 
.0341 
.2918 

*  To  obtain  linear  coefficient  divide  by  10,000. 
t  To  obtain  cubical  coefficient  divide  by  1000. 


APPENDIX  A 


301 


TABLE  VIII 

TABLE  OF  MELTING-  AND  BOILING-POINTS  AND 
LATENT  HEATS 


Substance. 

Melting 
Point. 
Deg.  C. 

Latent  Heat  of  Fusion. 

Boiling 
Point, 
Deg.  C. 

Latent  Heat 
of  Vaporiza- 
tion. 

B.T.U 

K 

Ft.-lbs. 
per  Lb. 

Cal. 
per 
Gm. 

Ergs 
per  Gm. 

B.T.U 

Cal. 

Alcohol,  ethyl  

-112 



77.9 
66 
2300 
-34 
1535* 
80.1 
1300 
61 
746 

2100 

2530* 
-252.5 
about 
2420 

1800 
357 

-193 
-182.5 
2450* 
f  2400* 
I  2040 
440 
338 

1450  to 
1600 
3700* 
930 

100 

396 

529 
167 

112 
970 

202 

294 
92.9 
46 

62 
539 

658 
-75.5 
632 

... 

76.8 
108 



Ammonia  
Antimony  

22.7 
29.2 

24.7 

268 
7.1 
321 
-80 

1084 
1064 
1064 
-257 

1510  | 

327 
-39 
1427 
—214 

17,640 
22,680 
19,180 

12.6 
16.2 
13.7 

52.9X107 
68.0X107 
57.5X107 

Bromine  

Carbon  dioxide.  . 
Copper  (in  reduc- 
ing atmosphere) 
Copper  (in  air)  .  .  . 
Gold  

28.8 

22,400 

16.0 

67.2X107 

'  '      cast  gray  .  .  . 
'  '      cast  white  .  . 
Lead  

41.4 
59.4 
9.7 
5.4 
8.3 

32,200 
46,200 
7,560 
3,920 
6,440 

23.0 
33.0 
5.4 

2.8 
4.6 

96.6X107 
138.6X107 
22.7X107 
11.8X107 
19.3X107 

Nickel      

—238 

Platinum  

1740 
about 
962 
115 
10  4 

49.0 
38.0 

38,080 
29,540 

27.2 
21.1 

9  4 

114.2X107 
88.6X107 

Silver    (free  from 
oxygen)  
Sulphur  

Tantalum  
Tin      

2910 
about  f 
232  I 
3080 
about 
419 
0.0 

25.7 

20,020 

14.3 

69.1X107 

Zinc 

50.6 
144 

39,340 
112,000 

28.1 
80 

118.2X107 
336.0X107 

Water  (pure)  .... 

*  Sublimes. 


302 


HEAT 


TABLE  IX* 


STEAM  TABLES 


I 

Pressure, 
Lbs.  per 
Sq.in. 

2 

Temp. 
Fahr. 

3 

Total 
Heat 
Energy. 

4 

Specific 
Volume, 
Cu.ft. 
per  Lb. 

5 

Density, 
Lbs.  per 
Cu.ft. 

6 

Heat 
Energy 
of 
Liquid. 

7 

Energy 
of 
Vapori- 
zation. 

8 

Inter- 
nal 
Heat 
Energy. 

9 

Exter- 
nal 
Work. 

.088 

32.00 

1071.7 

3308 

.000302 

0.0 

1071.7 

1017.5 

54.2 

.100 

35.02 

1073.2 

2952 

.000340 

3.0 

1070.2 

1015.6 

54.6 

.150 

45.42 

1078.2 

2005 

.000498 

13.5 

1064.7 

1009.1 

55.6 

.200 
.300 

53.14 

64.48 

1081.8 
1087.3 

1526 
1039 

.000650 
.000995 

21.2 
32.6 

1060.6 
1054.7 

1004.2 
997.1 

56.4 
57.6 

.400 

72.91 

1091.2 

790 

.001265 

41.0 

1050.2 

991.8 

58.5 

.500 

79.68 

1094.5 

640 

.001562 

47.8 

1046.7 

987.4 

59.3 

.600 

85.35 

1097.1 

538 

.001822 

53.4 

1043.7 

983.9 

59.8 

.700 

90.18 

1099.4 

443 

.002119 

58.3 

1041  .  1 

980.8 

60.3 

.800 

94.48 

1101.4 

411 

.002435 

62.6 

1038.8 

978.0 

60.7 

.900 

98.34 

1102.9 

367.7 

.002719 

66.3 

1036.6 

975.5 

1.1 

1.00 

101.8 

1104.5 

331.1 

.003002 

69. 

1034.7 

973.1 

61.6 

1.25 

109.4 

1107.8 

269.5 

.003710 

77.4 

1030.4 

968.1 

62.3 

1.50 

115.8 

1110.6 

227.0 

.004405 

83.8 

1026.8 

963.8 

63.0 

1.75 

121.3 

1112.9 

196.4 

.00509 

89.3 

1023.6 

960.0 

63.6 

2.00 

126.2 

1116.1 

173.1 

.00578 

94.2 

1021.9 

957.8 

64.1 

2.50 

134.5 

1118.7 

140.5 

.00712 

102.5 

1016.2 

951.3 

65.0 

3.00 

141.5 

1121.8 

118.4 

.00845 

109.6 

1012.2 

946.4 

65.8 

3.50 

147.6 

1125.2 

102.5 

.00975 

116.6 

1008.6 

942.3 

66.4 

4.00 

153.0 

1126.5 

90.4 

.01106 

121.0 

i005.5 

938.6 

66.9 

5.00 

162.3 

1130.3 

73.3 

.01364 

130.3 

1000.0  |  932.1 

67.9 

6.00 
7.00 

170.1 
176.8 

1133.6 
1136.3 

61.9 
53.6 

.01616 
.01866 

138.1 
144.9 

995.5      926.8 
991.4     922.0 

68.7 
69.4 

8.00 

182.9 

1138.7 

47.26 

.02116 

150.9 

987.8 

917.8 

70.0 

9.00 

188.3 

1140.9 

42.36 

.02362 

156.4 

984.5 

914.0 

70.5 

10.0 

193.2 

1142.7 

38.37 

.02606 

161.3 

981.4 

910.4 

71.0 

11.0 

197.7 

1144.5 

35.11 

.02848 

165.9 

978.6 

907.1 

71.5 

12.0 

202.0 

1146.1 

32.40 

.03088 

170.1 

976.0 

904.1 

71.9 

13.0 

205.9 

1147.7 

30.06 

.03327 

174.1 

973.6 

901.3 

72.3 

14.0 

209.6 

1149.0 

28.03 

.03567 

177.8 

971.2 

898.6 

72.6 

15.0 

213.0 

1150.4 

26.28 

.03805 

181.3 

969.1 

896.2 

72.9 

16.0 

216.3 

1151.6 

24.74 

.04042 

184.6 

967.0 

893.8 

73.2 

17.0 

219.4 

1152.8 

23.38 

.04277 

187.8 

965.0 

891.5 

73.5 

*  Adapted  from  Professor  Cecil  H.  Peabody's^"  Tables  of  the  Properties  of  Steam." 


APPENDIX  A 


303 


TABLE  IX — Continued 


1 

Pressure, 
Lbs.  per 
Sq.in. 

2 

Temp. 
Fahr. 

3 

Total 
Heat 
Energy. 

4 

Specific 
Volume, 
Cu.ft. 
per  Lb. 

5 

Density 
Lbs.  per 
Cu.ft. 

6 

Heat 
Energy 
of 
Liquid. 

7 

Energy 
of 
Vapori- 
zation. 

8 

Inter- 
nal 
Heat 
Energy. 

9 

Exter- 
nal 
Work. 

18.0 

222.4 

1153.9 

22.17 

.04511 

190.8 

963.1 

889.3 

73.8 

19.0 

225.2 

1154.9 

21.07 

.04746    193.7 

961.2 

887.2 

74.0 

20.0 

228.0 

1155.8 

20.09 

.04978    196.4 

959.4 

885.1 

74.3 

21.0 

230.6 

1156.8 

19.19 

.0521 

199.1 

957.7 

883.1 

74.6 

22.0 

233.1 

1157.6 

18.37 

.0544 

201.6 

956.0 

881.2 

74.8 

23.0 

235.5 

1158.5 

17.62 

.0568 

204.1 

954.4 

879.4 

75.0 

24.0 

237.9 

1159.3 

16.92 

.0591 

206.4 

952.9 

877.7 

75.2 

26.0 

242.3 

1160.8    15.70 

.0637 

210.9 

949.9 

874.4 

75.5 

28.0 

246.4 

1162.2    14.67 

.0682 

215.1 

947.1 

871.2 

75.9 

30.0 

250.3 

1163.5    13.74 

.0728 

219.1 

944.4 

868.2 

76.2 

32.0 

254.1 

1164.7    12.93 

.0773 

222.9 

941.8 

865.2 

76.6 

34.0 

257.6 

1165.9    12.21 

.0819 

226.5 

939.4 

862.5 

76.9 

36.0 

261.0 

1167.0    11.58 

.0864 

229.9 

937.1 

859.9 

77.2 

40.0 

267.3 

1169.0 

10.49 

.0953 

236.4 

932.6 

855.0 

77.6 

45.0 

274.5 

1172.2 

9.387 

.1065 

244.7 

927.5 

849.3 

78.2 

50.0 

281.0 

1173.2 

8.507 

.1176 

250.4 

922.8 

844.1 

78.7 

55.0 

287.1 

1175.0 

7.778 

.1286 

256.6 

918.4 

839.2 

79.2 

60.0 

292.7 

1176.7 

7.166 

.1395 

262.4 

914.3 

834.7 

79.6 

65.0 

298.0 

1178.2 

6.647 

.1504 

267.8 

910.4 

830.4 

80.0 

70.0 

303.0 

1179.5 

6.199 

.1613     272.9 

906.6 

826.3 

80.3 

80.0 

312.1 

1182.0 

5.466 

.1829 

282.2 

899.8 

818.9 

80.9 

90.0 

320.3 

1184.2!     4.886 

.2047 

290.7 

893.5 

812.1 

81.4 

100.0 

327.9  11186.1      4.432 

.2256 

298.5 

887.6 

805.7 

81.9 

110.0 

334.8 

1187.7 

4.047 

.2471 

305.6 

882.1 

799.7 

82.4 

120.0 

341.3 

1189.2 

3.723 

.2686 

312.3 

876.9 

794.2 

82.7 

130.0 

347.4 

1190.7 

3.451 

.2898 

318.6 

872.1 

789.0 

83.1 

140.0 

353.1 

1191.8 

3.220 

.3106 

324.4 

867.4 

784.0 

83.4 

150.0 

658.5 

1193.0 

3.014 

.3318 

330.0 

863.0 

779.3 

83.7 

160.0 

363.6 

1194.1 

2.834 

.3528 

335.3 

858.8 

774.9 

83.9 

180.0 

373.2 

1196.1 

2.531 

.3951 

345.2 

850.9 

766.5 

84.4 

200.0 

381.9 

1197.8 

2.288 

.4371 

354.3 

843.5 

758.8 

84.7 

225.0 

391.9 

1199.6 

2.043 

.4894 

364.7 

834.9 

749.8 

85.1 

250.0 

401.1 

1201  .  1 

1.845 

.542 

374.2 

826.9 

741.5 

85.4 

275.0 

409.6 

1202.6 

1.681 

.595 

383.1 

819.5 

734.0 

85.5 

300.0 

417.5 

1203.7 

1.542 

.649 

391.3 

812.4 

726.8 

85.6 

336.0 

427.9 

1205.2 

1.377 

.726 

402.2 

803.0 

717.4 

85.6 

304 


HEAT 


TABLE  X* 
PRESSURE-ENTROPY 


Tern. 
Fahr. 

Pres- 
sure 
in 
Lbs. 
per 
q.  in. 

1.52 

1.58 

1.64 

Qual- 
ity. 

Total 
Energy. 

Spe- 
cific 
Vol. 

Qual- 
ity. 

Total 
Energy. 

Spe- 
cific 
Vol. 

Qual- 
ity. 

Total 
Energy. 

Spe- 

C1JC 

Vol. 

420 

309 

10.7 

1213 

1.54  101 

1268 

1.78 

224 

1331 

2.09 

400 

247 

991 

1193 

1.85  71.6 

1246 

2.11 

186 

1306 

2.46 

390 

220 

982 

1184 

2.05 

57.9 

1236 

2.30 

167 

1294 

2.68 

380 

196 

972 

1174 

2.27 

43.9 

1225 

2.52 

149 

1281 

2.92 

370 

173 

966 

1164 

2.53 

30.0 

1214 

2.77 

130 

1269 

3.20 

360 

153 

955 

1154 

2.83  16.3 

1203 

3.05 

112 

1257 

3.50 

350 

135 

946 

1144 

3.16   2.7 

1193 

3.36 

94.7 

1244 

3.86 

340 

118 

938 

1134 

3.55 

992 

1182 

3.75 

77.1 

1232 

4.28 

330 

103 

929 

1124 

4.01 

983 

1171 

4.24 

59.8 

1219 

4.74 

320 

89.6 

921 

1113 

4.52 

973 

1160 

4.78 

42.6 

1207 

5.27 

310 

77.6 

913 

1103 

5.13 

964 

1149 

5.42 

25.4 

1195 

5.86 

300 

67.0 

904 

1092 

5.85 

955 

1137 

6.17 

8.1 

1183 

6.56 

290 

57.5 

896 

1081 

6.68 

945 

1126 

7.05 

995 

1171 

7.42 

280 

49.2 

889 

1070 

7.68 

937 

1114 

8.09 

985 

1159 

8.50 

270 

41.8 

881 

1059 

8.85 

928 

1102 

9.32 

975 

1146 

9.80 

260 

35.4 

873 

1047 

10.3 

919 

1091 

10.8 

965 

1134 

11.3 

250 

29.8 

865 

1036 

12.0 

910 

1079 

12.6 

955 

1121 

13.2 

240 

25.0 

857 

1024  . 

14.0 

902 

1066 

14.7 

946 

1108 

15.4 

230 

20.8 

850 

1013 

16.5 

893 

1054 

17.3 

936 

1095 

18.1 

220 

17.2 

842 

1001 

19.5 

885 

1042 

20.5 

927 

1082 

21.5 

212 

14.7 

836 

991 

22.4 

878 

1031 

23.5 

919 

1072 

24.6 

200 

11.5 

827 

977 

27.8 

868 

1016 

29.2 

908 

1056 

30.5 

180 

7.51 

812 

952 

40.8 

851 

990 

42.7 

890 

1028 

44.7 

160 

4.73 

797 

926 

61.5 

834 

964 

64.4 

871 

1001 

67.3 

150 

3.72 

790 

913 

76.5 

824 

950 

80.0 

862 

987 

83.5 

145 

3.28 

786 

907 

85.6 

822 

943 

89.6 

858 

979 

93.5 

140 

2.88 

782 

900 

96.0 

818 

936 

100 

853 

972 

105 

135 

2.53 

778 

894 

108 

813 

929 

113 

848 

965 

118 

130 

2.22 

774 

887 

122 

809 

922 

127 

844 

958 

133 

125 

1.94 

771 

880 

137 

805 

915 

144 

839 

950 

150 

120 

1.69 

767 

873 

156 

801 

908 

163 

835 

943 

169 

115 

1.47 

763 

867 

177 

796 

901 

185 

830 

936 

192 

110 

1.27 

759 

860 

201 

792 

894 

210 

825 

928 

220 

105 

1.10 

755 

853 

230 

788 

887 

240 

821 

921 

250 

100 

.95 

751 

846  '264 

784 

879 

275 

816 

913 

286 

95 

.81 

747 

839 

303 

779 

872 

315 

811 

906 

328 

90 

.70 

743 

832 

349 

775 

865 

364 

807 

898 

379 

85 

.60 

739 

825  402 

771 

858 

419 

802 

890 

436 

80 

.51 

736 

818 

466 

766 

850 

486 

797 

883 

505 

70 

.363 

728 

803 

632 

758 

835 

658 

789 

867 

684 

60 

.256  720 

789 

849 

749 

820 

884 

779 

851 

919 

32 

.089 

697 

747 

725 

776 

752 

806 

*  Adapted  from  Professor  Cecil  H.  Peabody's  "Tables  of  the  Properties  of  Steam." 


APPENDIX  A 
TABLE  X— Continued 


305 


1.70 

1.76 

1.82 

Pres- 

Qual- 
ity. 

Total 
Energy. 

Spe- 
cific 
Vol. 

Qual- 
ity. 

Total 
Energy. 

Spe- 
cific 
Vol. 

Qual- 
ity. 

Total 
Energy. 

Spe- 
cific 
Vol. 

sure 
in 
Lbs. 

Tern. 
Fahr. 

309 

420 

247 

400 

295 

1358 

3.08 

220 

390 

274 

1344 

3.36 

196 

380 

252 

1330 

3  68 

173 

370 

231 

1316 

4.04 

153 

360 

210 

1302 

4.44 

135 

350 

189 

1288 

4.91 

118 

340 

167 

1274 

5.44 

103 

330 

146 

1260 

6.05 

266 

1319 

6.90 

89  6 

320 

125 

1246 

6  75 

241 

1303 

7  68 

77.6 

310 

104 

1232 

7.54 

217 

1287 

8.60 

67.0 

300 

83  6 

1218 

8.46 

192 

1271 

9.66 

57.5 

290 

62.9 

1204 

9.51 

168 

1255 

10.9 

287 

1313 

12.4 

49.2 

280 

42.1 

1191 

10.07 

144 

1240 

12.3 

260 

1296 

14.0 

41.8 

270 

21.6 

1177 

12.2 

120 

1225 

14.0 

232 

1278 

15.9 

35.4 

260 

0.6 

1164 

13.8 

96.1 

1209 

15.9 

205 

1261 

18.2 

29.8 

250 

990 

1150 

16.1 

72.0 

1194 

18.2 

177 

1244 

20.7 

25.0 

240 

979 

1137 

19.0 

48.0 

1179 

20.8 

149 

1226 

23.9 

20.8 

230 

969 

1123 

22.4 

24.2 

1164 

24.0 

122 

1209 

27.6 

17.2 

220 

961 

1112 

25.7 

5.0 

1152 

27.0 

100 

1196 

31.1 

14.7 

212 

949 

1095 

31.9 

989 

1135 

33.3 

68.3 

1176 

37.4 

11.5 

200 

929 

1067 

46.6 

967 

1105 

48.6 

14.6 

1144 

51.2 

7.51 

180 

909 

1038 

70.1 

946 

1075 

73.0 

983 

1112 

75.9 

4.73 

160 

899 

1023 

87.1 

935 

1060 

90.6 

971 

1096 

94.1 

3.72 

150 

894 

1016 

97.4 

929 

1052 

101 

965 

1088 

105 

3.28 

145 

889 

1008 

109 

924 

1044 

113 

960 

1080 

118 

2.88 

140 

884 

1001 

123 

919 

1036 

128 

954 

1072 

132 

2.53 

135 

879 

993 

138 

913 

1028 

144 

948 

1064 

149 

2.22 

130 

874 

985 

156 

908 

1021 

162 

942 

1056 

168 

1.94 

125 

'  869 

978 

176 

903 

1013 

183 

936 

1047 

190 

1.69 

120 

864 

970 

200 

897 

1005 

208 

931 

1039 

216 

1.47 

115 

858 

962 

,228 

892 

996 

236 

925 

1031 

245 

1.27 

110 

853 

955 

260 

886 

988 

270 

919 

1022 

280 

1.10 

105 

848 

947 

298 

881 

980 

309 

913 

1014 

320 

.95 

100 

843 

939 

341 

875 

972 

354 

907 

1005 

367 

.81 

95 

838 

931 

393 

870 

964 

408 

902 

997 

423 

.70 

90 

833 

923 

453 

865 

956 

470 

896 

988 

487 

.60 

85 

828 

915 

|525 

859 

947 

545 

890 

980 

564 

.51 

80 

818 

899 

710 

849 

931 

737 

879 

962 

763 

.363 

70 

808 

883 

|954 

838 

914 

988 

867 

945 

.256 

60 

780 

836 

807 

865 

835 

895 

.089 

32 

306 


HEAT 


TABLE  XI 


Pressure  in  Ibs.  per  sq.in. 

14.2 

50 

100 

150 

200 

250 

300 

Temp,  superheat  F.  212°.  . 

.46 

"    300°  . 

.46 

.51 

400°  . 

.46 

.50 

.54 

.60 

.67 

500°  . 

.46 

.49 

.53 

.55 

.59 

.63 

.67 

600°  . 

.47 

.49 

.51 

.53 

.55 

.57 

.59 

«    «     700o 

.47 

.49 

.51 

.52 

.53 

.55 

.56 

TABLE  XII 
TEMPERATURES  OF  HOT  BODIES 


Source. 

Degree  C. 

Observer  and  Method. 

Incandescent  electric  lamp 
(carbon)  

1800 

Lg  Chatelier  optical  pyrometer 

Arc  lamp  
Arc  lamp 

4100 
3760 

(  (                   it 
Fery  heat  radiation  pyrometer 

Thermit  in  mold 

2500 

<  <            it               <  < 

Bunsen  flame,  open  ....... 
Bunsen  flame,  closed  
Acetylene  flame  .... 

1870 
1710 
2550 

Fery,  spectroscopic  method 

i  <              a                 u 

(i             tt                 (  ( 

Oxy-hydrogen  flame  
Melting-point  of  tantalum  . 

Melting-point  of  tungsten.  . 
Temperature  of  sun  
Temperature  of  sun  

2420 
3000 

3200 
7600 
7500 

(  i              1  1                 1  1 

Waidner  and  Burgess,  optical 
pyrometer 
do.             do. 
Le  Chatelier,  optical  pyrometer 
Fery,  heat-radiation  pyrometer 

TABLE  XIII 

WAVE   LENGTHS  MiUioath,  of  cm. 

Shortest  ultra-violet  waves 10 

Shortest  visible  waves  (violet),  about 38 

Violet,  about 40 

Blue 45 

Green 52 

Yellow 57 

Red 65 

Longest  visible  waves  (red) 75 

Longest  waves  in  solar  spectrum,  more  than ....  530 

Longest  waves  transmitted  by  fluorite 950 

Longest  waves  by  selective  reflection  from  rock 

salt 5,000 

By  reflection  from  potassium  chloride 6,120 

Shortest  electric  waves 600,000 


APPENDIX  A 


307 


TABLE  XIV 
THERMAL  CONDUCTANCE* 


Temp. 
Range, 
Cent., 
Deg. 

Ohms,  Thermal 
Resistance. 

Thermal  Conductance  or 
Conductivity. 

Inch, 
Cube. 

Cm. 
Cube. 

Mho. 

Cm.  Cube 
Calorie 
Unit. 

Britisht 
Units 
per  Hr. 

Air  
Aluminium  

at  0 

2000 
.73 
353 
1060 
44 
53 
160 

2.7 
1530 
0.27 
220 
42 
675 
1890 
0.66 
1.6 
0.60 
7.7 
0.55 
2.0 
2.8 
1410 
2680 
1600 
0.24 
1.59 
2700 
500 
920 
1460 
7100 
2600 
1600 
2100 
.81 

.0005 
1.5 
.0028 
.0009 
.023 
.019 
.0063 

.37 
.00065 
3.7 
.0046 
.024 
.0015 
.0005 
1.5 
.63 
1.67 
.13 
1.8 
.5 
.36 
.00071 
.00037 
.00063 
4.20 
.63 
.00037 
.0020 
.0011 
.0007 
.00014 
.00038 
.00063 
.00048 
1.23 

.0001 
.35 
.0007 
.0002 
.006 
.0045 
.0014 

.088 
.00017 
.85 
.0011 
.0057 
.00036 
.00012 
.36 
.15 
.40 
.031 
.43 
.12 
.085 
.00017 
.00009 
.00015 
1.00 
.153 
.00009 
.00047 
.00026 
.00016 
.00003 
.00009 
.00015 
.00011 
.295 

.35 

1000 
1.96 
.65 
16 
13 
4.4 

260 
.45 
2600 
3.2 
17 
1.0 
.35 
1000 
440 
1200 
90 
1200 
350 
250 
.49 
.25 
.44 
3900 
440 
.25 
1.38 
.76 
.48 
.10 
.26 
.44 
.33 
850 

f  From 

139 
416 
17 
21 
62 

1.05 
603 
0.11 
87 
16 
263 
745 
0.26 
0.63 
0.24 
3.0 
0.22 
0.79 
1.1 
554 
1060 
600 
0.09 
.63 
1070 
200 
360 
572 
2800 
1000 
620 
600 
.32 

Asbestos  <  ^ 

Boiler  scale     

at  60 

B™k(forom  •.•.:::::: 

Carbon  (electrode)..  .  . 
Charcoal                .... 

100  to 
360 
at  ,50 
0  to  100 

Copper  .  . 

Glass    

Ice  

Infusorial  earth  {  f  rom 

f  /-+          )  From  . 

Cast    (    to     .. 
CI.L    i    f  From  .  . 



Iron    Steel    {     to 

Wrought  (Frt°om 
Lead              

Magnesia,  calcined.  .  .  . 
Rubber,  hard  

20tol55 

Sawdust 

Silver  .  .    . 

0  to  100 

Tin  

Wood,  pine 

'  '      fir  along  fiber. 

fir  across  fiber  .  . 
TTT     i                f  From 



Wool,  cotton  <     tg 

'  '       mineral  
f  From. 

itois 

,sheeP  t    to      . 
Zinc 

*  All  the  values  in  this  table  are  approximations. 
t  B.T.U.  per  hr.  per  sq.ft.  area  per  in.  thickness. 


APPENDIX  B 

NOTE  ON  CORRECTION  OF  BAROMETER  FOR 
TEMPERATURE 

READINGS  taken  directly  from  a  barometer  must  be  cor- 
rected for  several  errors  before  being  used  in  very  accurate 
determinations.  Among  the  corrections  necessary  are  those 
afor  temperature,  for  capillarity,  and  for  vapor  pressure  in 
the  tube  above  the  mercury.  Of  these,  the  correction  for 
temperature  is  the  most  important  and  is  the  only  one 
which  will  be  made  in  any  of  the  experiments  given  in 
this  course,  unless  the  student  is  otherwise  directed  by  the 
instructor. 

To  read  the  laboratory  barometer  and  correct  this 
reading,  proceed  as  follows:  First  adjust  the  height  of 
mercury  in  the  cistern  until  the  surface  is  just  in  contact 
with  the  point  of  the  ivory  index.  Then  read  the  height  of 
the  mercury  column  with  the  vernier  of  the  instrument,  and 
take  the  temperature  of  the  mercury  as  given  by  the  ther- 
mometer in  the  case.  The  true  height  of  the  barometer  is 
its  height  at  0°  C.  Since  mercury  expands  .00018  of  its 
volume  for  each  degree  C., 

reading  at  0°  C.  =  /i-.00018K 

when  t  =  temperature  (centigrade)  of  the  mercury  as  obtained 
from  the  thermometer  of  the  instrument,  and  h  =  observed 
height. 

A  further  correction  is  made  necessary  by  the  expansion 
of  the  brass  scale  if  it  be  graduated  at  0°  C.  Brass 

308 


APPENDIX  B  309 

expands  .000019  of  its  length  for  each  degree  C.    Making 
this  correction  we  have: 

true  height  =  h  -  (.00018  -  .000019) hi. 

PROBLEM.    Barometer   reads    14.48    Ibs.    at    23.4°    C. 
Reduce  to  0°  C. 


APPENDIX  C 

SIGNIFICANT  FIGURES 

(Revised  and  reprinted  with  permission  from  Jameson's  "  Mechanics." 
Longmans,  Green  &  Co.). 

IN  practical  computation,  figures  should  not  be  used 
blindly  according  to  the  simple  rules  of  arithmetic.  We 
often  use  what  we  sometimes  call  round  numbers  when 
we  are  working  roughly  and  not  with  absolute  certainty. 
In  industrial  and  technical  computations  we  are  never 
absolutely  exact.  Approximate  information  and  approxi- 
mate results  are  all  we  ever  have.  The  more  scientifically 
we  work  the  more  carefully  must  we  recognize  and  indicate 
the  degree  of  accuracy  of  our  work. 

Significant  figures  are  figures  which  we  know  to  represent 
with  reasonable  certainty  some  real  condition  or  quantity. 
Significant  figures  give  all  the  information  which  we  have 
without  giving  any  of  which  we  are  not  reasonably  certain. 
In  other  words,  they  are  figures  which  really  mean  some- 
thing. 

The  student  must  observe  carefully  the  following  rules 
in  all  laboratory  work  and  reports.  These  same  rules  should 
always  be  applied  to  recording  scientific  or  technical  data. 
These  rules  must  be  applied,  however,  with  judgment,  as 
they  are  intended  merely  as  a  guide  to  judgment  rather 
than  as  orders  to  be  followed  blindly.  The  following  exam- 
ples illustrate  the  use  of  significant  figures: 

I.   RECORDING  READINGS 

In  general,  scales,  etc.,  are  to  be  read  to  tenths  of  the 
smallest  divisions  marked  on  the  instrument.  The  last 

310 


APPENDIX  C  311 

figure  entered  in  the  record  is  thus  assumed  always  to  be 
an  estimation  and  therefore  doubtful. 

Example  1.  15.57  cms.  means  that  a  distance  was  meas- 
ured by  a  scale  subdivided  to  millimeters,  and  that  the 
observer  estimated  the  seven;  thus  the  distance  is  known 
to  be  between  15.5  and  15.6,  and  estimated  to  be  -£$  the 
way  between  these  two  values.  It  is  misleading,  and 
furnishes  only  a  clue  to  what  we  actually  know  about  this 
distance  to  record  it  as  15.6  or  15.570  cm. 

Example  2.  A  distance  is  being  measured  with  a  rule 
subdivided  to  tenths  of  inches.  The  observer  finds  the  dis- 
tance to  be  as  nearly  exactly  seven  inches  as  he  can  dis- 
tinguish. This  should  be  recorded  7.00  in.  (not  7.0  or  7  ins.). 
Why? 

Example  3.  A  balance  is  capable  of  weighing  an  object 
to  .01  gm.  and  .001  gm.  can  be  estimated.  Notice  the 
correct  records  for  following: 

Eight  gms 8.000  gms. 

Eight  and  J  gms 8.250  gms. 

Eight  and  Tf^  gms 8.070  gms. 

Eight  and  -?-/-$-$  gms 8.008  gms. 

Eight-tenths  gm 800  gm. 

In  general  a  series  of  readings  made  with  the  same  in- 
strument should  all  show  the  same  number  of  places  filled 
in  to  the  right  of  the  decimal  point  even  if  one  or  all  these 
places  are  zeros.  Why? 

It  is  often  convenient  to  express  in  decimal  form,  read- 
ings taken  from  scales  divided  into  halves  of  units,  quar- 
ters, eighths,  etc.  In  all  such  cases,  retain  only  as  many 
places  in  the  decimal  as  correspond  approximately  to  the 
same  degree  of  precision  as  would  be  expressed  by  the 
fraction,  i.e.,  to  the  nearest  half  unit,  to  the  nearest  quar- 
ter, etc.  If  the  first  decimal  figure  rejected  is  5  or  greater, 
call  the  preceding  figure  one  larger  than  before.  For 
example: 


312  HEAT 

\  —  .5  when  the  reading  merely  means  that  it  is  somewhere 

between  zero  and  unity. 
If  by  \  the  observer  is  certain  that  the  reading  is  nearer 

\^  than  it  is  fa  or  ^,  then  the  true  decimal  equiv. 

=  .50. 
\  =  .3  except  when  the  observer  is  sure  that  it  is  nearer  J$ 

than  is  -f$  or  ^  when  the  true  decimal  equiv.  =  .33. 
i  =  .3,  but  when  the  values  are  such  thatj>^  but  <H> 

then  decimal  equiv.  =  .25. 

-|  =  .2  and  not  .20  except  under  similar  conditions  as  above. 
£  =  .2  and  not  .1667,  etc. 

J  =  .l.  i  =  -4.  f  =  .7. 

^  =  .06.  |  =  .6.  f  =  .8. 

A  =  -03.  I  =  .9.  A  =  .19. 

II.  USE  OF  DATA  IN  CALCULATIONS 

Wherever  the  figure  following  the  doubtful  (last  re- 
tained) figure  is  5  or  greater  than  5,  increase  the  doubtful 
figure  by  unity.  Thus,  if  but  three  figures  are  to  be  kept, 
15.75,  15.76,  15.77,  15.78,  and  15.79  would  all  be  entered 
15.8. 

Notice  especially  that  the  location  of  the  decimal  point 
has  nothing  to  do  with  significant  figures.  Thus,  275,  27.5, 
2.75,  .275,  .0275,  .00275,  etc.,  are  all  results  expressed  to  the 
same  degree  of  precision,  and  in  each  there  are  three  and 
only  three  significant  figures,  the  5  being  the  doubtful  figure 
in  each. 

Averages.  In  averaging  a  series  of  determinations,  in 
general,  retain  in  the  result  the  same  number  of  significant 
figures  as  in  any  one  item. 

But  if  a  large  number  of  items  closely  agreeing  with  each 
other  are  averaged,  the  result  may  contain  one  more  sig- 
nificant figure  than  any  item. 

Multiplication.  After  the  operation,  keep  in  the  result 
as  many  figures,  counting  from  the  left,  as  there  are  sig- 


APPENDIX  C  313 

nificant  figures  in  the  factor  having  the  lesser  number  of 
significant  figures. 

Division.  In  dividing  one  number  by  another,  keep 
in  the  quotient  as  many  figures  as  there  are  significant 
figures  in  the  number  having  the  lesser  number  of  signifi- 
cant figures.  Continue  the  divisions  only  far  enough  to 
determine  the  required  figures. 

Note  on  Multiplication  and  Division.  Ciphers  immediately 
following  the  decimal  point,  when  there  are  no  figures  to  the  left  oj 
the  point,  do  not  count  as  significant.  Study  the  following  examples : 

(a)  15.75     X3.08       =48.5. 
(6)       .096  X  .096     =     .0092. 

(c)  .1523X  .00113=     .000172. 

(d)  720        X3.1         =2200. 

The  cipher  in  cases  (6),  (c),  and  (d)  are  not  significant. 

(e)  .900       X.800      =.720. 

All  the  ciphers  in  this  case  are  significant. 
(/)   900        X800       =720,000. 

In  the  product  in  (/)  only  the  first  cipher  is  significant. 
It  is  necessary  to  add  the  other  three  to  express  the  number 
properly. 

(flf)  325.6  ^72.5  =4.49. 

(h)        .0007859  -M  57    =   .00000500. 

Use  of  Pure  Numbers,  Constants,  etc.  In  using  pure 
numbers  and  constants  such  as  3.1416,  .7854,  etc.,  do 
not  employ  more  figures  than  there  are  significant  figures 
in  the  experimental  data  which  are  used  with  the  constants 
in  the  same  calculation.  Thus  if  the  diameter  of  a  circle 
is  measured  as  4.51,  the  area  is  4.51  X4.51X. 785  =  15.9. 
The  use  of  more  numbers  in  the  constant  lengthens  the 
computation  and  gives  no  better  result.  Why? 


APPENDIX  D 

CURVES 

CURVES  are  used  to  show  a  large  amount  of  data  in  a 
way  to  make  the  significance  of  the  information  as  a  whole 
appeal  to  the  eye.  Curves  are  like  a  picture  of  the  data 
in  that  they  enable  one  to  view  the  subject  matter  as  a 
whole  and  also  to  see  each  detail. 

Generally  curves  show  what  happens  to  two  quantities 
which  are  varying.  In  the  course  of  experiments  in  the 
laboratory  the  student  may  have  occasion  to  adjast  or 
vary  the  temperature  of  a  body,  the  energy  in  a  body, 
or  some  other  property  or  factor  within  his  control.  The 
quantity  which  the  student  alters  is  called  the  independent 
variable  and  is  usually  represented  algebraically  by  the 
letter  X. 

As  a  result  of  the  change  which  takes  place  in  the  quan- 
tity1 which  is  represented  by  X  a  change  may  take  place  in 
some  other  factor  or  property  of  matter,  and  this  second 
variable  is  usually  represented  by  Y.  Thus  if  X  repre- 
sented .  the  temperature  of  a  gas,  then  Y  might  represent 
the  volume  of  the  gas,  the  density  of  the  gas,  or  any  other 
property  of  the  gas  which  was  affected  by  a  change  of 
temperature. 

(The  following  is  a  revision  by  permission  of  pp.  305  to 
313  of  Jameson's  "  Mechanics,"  Longmans,  Green  &  Co.) 

Coordinate  Axes.  The  position  of  a  single  point  in 
space  may  be  fixed  by  reference  to  two  known  straight 
lines  intersecting  at  right  angles  in  the  same  plane  as  the 
point.  Thus  PI  has  its  position  defined  by  OX  and  OY 
of  Fig.  78.  Such  lines  are  known  as  coordinate  axes. 

314 


APPENDIX  D 


315 


X 

- 

- 

— 

— 

E 

P 

I 

i 

i 

_„    2     L    i          < 

1         10       .  »  .     - 

Also  the  position  of  a  series  of  points  which  go  to  make 
up  a  line  may  be  expressed  in  a  similar  way. 
i      The  horizontal  line  (OX)  is  known  as  the  axis  of  abscissae 
or    "  X  axis,"    the  vertical      v 
line    (OF)    as    the    axis    of 
ordinates  or  "  F  axis."     The 
abscissa    of    a    point    is  its 
horizontal  distance  from  OF; 
its   ordinate   is    the  vertical 
distance   from   OX.      These 
given,    the   position   of    the 
point   is  determined.     Thus 
P  is  that  point  which  has  an 
abscissa  of  3,  an  ordinate  of  FIG.  78. 

5,  PI  the  point  which  has  abscissa  of  11,  ordinate  of  8,  etc. 

The  point  of  intersection  of  the  axes  is  called  the  Qrigin. 

For  convenience,  squared  or  cross-section  paper  is  used 
for  work  of  this  kind. 

Curves.  A  succession  of  related  points  may  be  con- 
nected by  a  smooth  line,  thus  constituting  a  "  curve." 
Such  curves  are  frequently  the  most  convenient  and  the 
clearest  way  of  representing  a  physical  law,  corrections 
for  errors  of  apparatus,  etc.  Suppose,  for  example,  that  it 
is  desired  to  show  the  relation  between  the  volume  of  1  Ib. 
of  air  and  the  temperature.  Changes  in  temperature  pro- 
duce changes  in  volume  according  to  the  following  data: 


Abs.  Temperature. 
461 
550 
625 
700 
775 
900 


Volume. 
12.4 
14.7 
16.8 
18.8 
20.7 
24.2 


Taking  the  absolute  temperature  expressed  in  some  con- 
venient scale  of  lengths,  as  abscissa,  and  the  corresponding 


316 


HEAT 


volumes,  similarly  expressed  as  ordinates,  a  series  of  points 
may  be  located  as  just  explained,  and  through  these  a  smooth 
line  may  be  drawn.  Inspection  of  the  curve  thus  produced 
(Fig.  79)  will  show  at  a  glance  information  which  could 
be  obtained  from  the  figures  only  on  more  extended  analysis. 
The  law,  "  Volume  is  proportional  to  absolute  tempera- 
ture "  is  seen  immediately,  from  the  nature  of  the  curve. 


-24 

^ 

/ 

—90 

^ 

2 

/ 

~t 

-o 
O 

—  5- 

S 

-16 

S 

' 

^ 

/ 

1v>_ 

j£ 

' 

, 

/ 

RELATION 

BETWEEN 

TEMPERATURE  AND  VOLUME 

OF 

1  LB.  OF  AlR  UNDER 

H.7  LBS.  PRESSURE 

$ 

/ 

' 



/ 

/ 

/ 

/ 



S 

/ 

A 

/ 

S 

\ 

i 

1 

JO 

2( 

)0 

'EMP!ERAT 

4( 

URE 

0 
N  AE 

500 

SOLllTE  F 

.DEGREE 

800 

NAME 

9 

X) 

1 

I 

D 

ATE 

CL 

ss 

FIG.  79. 

Whenever  the  curve  is  a  straight  line  and  passes  through 
the  origin,  the  quantity  plotted  on  the  X  axis  is  in  direct 
proportion  to  the  quantity  plotted  on  the  Y  axis.  If  the 
curve  is  a  straight  line  but  does  not  pass  through  the  origin, 
the  increase  in  X  is  in  proportion  to  the  increase  in  7. 
This  latter  proportion  may  be  either  direct  or  inverse.  (See 
the  following  discussion  of  the  "  Equation  of  a  Straight 
Line  "  for  a  proof  of  the  above.) 

Had  the  curve  turned  continuously  more  and  more 
toward  either  the  X  or  the  Y  axis,  showing  in  one  case  a 


APPENDIX  D  317 

progressive  increase,  in  the  other  a  progressive  decrease  in 
volume  with  increase  of  temperature,  or  had,  at  any  time,  a 
sudden  change  from  the  conditions  which  had  previously 
existed  occurred,  these  factors  would  have  been  brought  to 
the  attention  as  quickly. 

When  also,  as  here,  the  great  majority  of  points  lie  along 
a  straight  line  (or,  as  in  some  cases,  along  a  smooth  curve), 
any  experimental  errors  of  measurement  (as  in  the  volume 
for  625°  and  775°)  will  be  shown  at  once  by  the  fact  that 
these  points  lie  slightly  off  the  line.  In  all  such  cases, 
the  curve  should  be  drawn  as  nearly  as  may  be  through 
all  points,  and  leaving  as  many  points  on  one  side  as  on  the 
other. 

The  student  must  in  all  cases  use  his  judgment  in  draw- 
ing the  curve  and  consider  the  conditions  of  the  experi- 
ment and  the  general  physical  law  illustrated. 

It  is  not  necessary,  and  indeed  often  not  advisable,  that 
ordinates  and  abscissae  be  expressed  in  the  same  scale.  Of 
course,  for  the  same  curve  all  abscissas  must  be  in  one 
scale,  and  all  ordinates  in  one  scale.  In  general,  the  scale 
adopted  should  be  that  most  convenient  for  the  particular 
values  which  will  at  the  same  time  give  a  curve  as  large 
as  the  paper  will  permit. 

One,  two,  five,  or  ten  units  to  a  square  will  be  found  the 
best.  Avoid  the  use  of  three  or  seven  units  per  inch,  or 
other  inconvenient  subdivisions. 


GENERAL  DIRECTIONS  FOR  CURVE  PLOTTING 

1.  The  curve  sheet  should  have  all  lines  and  lettering 
done  neatly  in  either  very  hard  pencil  or  India  ink,  as 
directed  by  an  instructor.  Ordinary  black  ink  should  never 
be  used  on  a  curve  sheet.  If  several  curves  are  to  be 
drawn  on  the  same  sheet  it  is  permissible  to  use  a  different 
color  of  ink  for  each  curve. 


318  HEAT 

2.  The  heavy  line  one  inch  up  from  the  first  ruled  line 
from  the  bottom  and  the  heavy  line  one  inch  over  from  the 
left  side  are  to  be  taken  as  axes.  (An  exception  to  this 
may  be  made  when  the  inch  thus  sacrificed  is  needed.) 
The  origin,  i.e.,  the  intersection  of  vertical  and  horizontal 
axes,  should  be  near  the  lower  left-hand  corner. 

Each  axis  should  start  near  the  lower  left-hand  corner. 
The  paper  may  be  used  with  either  the  longer  or  shorter 
side  as  vertical  axis,  according  to  needs  of  the  curve. 
i  3.  The  scale  on  which  the  curve  is  plotted  should  be  so 
selected  as  to  make  the  curve  as  large  as  possible.  The 
curve  should  go  as  faf  to  the  right  and  as  high  on  the  paper 
as  the  selection  of  a  convenient  scale  will  allow. 

4.  Each  axis  should  be  marked : 

(a)  With  the  name  of  the  quantity,  the  amount  of 
which  is  represented  by  distances  along  it. 

For  example:   The  X  axis  might  represent  temperature. 

(6)  With  the  name  of  the  unit  in  which  the  quantity 
is  measured.  For  example:  If  the  X  axis  represents  tem- 
perature, the  unit  might  be  degrees  C.  The  student  would 
then  letter,  not  write,  along  the  ruled  line,  J  in.  below 
the  axis  line  the  following:  "  TEMPERATURE  IN  DEGREES  C." 

(5)  Each  inch  line  along  both  the  vertical  and  the  hori- 
zontal axis  should  be  numbered  with  the  numerical  value 
which  is  represented  by  that  distance.     No  other  figures 
are  to  be  written  on  the  axis  line  or  in  any  other  way  used 
in  locating  points  on  the  curve. 

(6)  The  points  are  to  be  located  by  a  pin  prick  in  the 
paper  and  a  circle  should  be  drawn  around  this  with  a  bow 
pen  to  enable  the  point  to  be  more  readily  found. 

(7)  The  curve  should  usually  be  a  smooth  line  drawn  as 
nearly  as  possible  through  all  points.     It  will  represent  the 
most  probable  average  of  the  observations,  and  any  single 
point  lying  at  a  distance  on  either  side  of  the  line  will  usually 
be  a  result  of  error  in  observations.      Of  course  judgment  . 
must  be  used  in  drawing  this  conclusion,  and  the  conditions 


APPENDIX  D  319 

of  the  experiment  and  the  nature  of  the  related  quantities 
of  the  curve  must  always  be  taken  into  account. 

In  locating  the  curves,  if  it  is  to  be  a  straight  line,  a 
rubber  band  will  be  found  helpful.  A  transparent  straight- 
edge will  be  found  still  better. 

The  curve  is  the  only  line  which  the  student  should  draw 
on  the  coordinate  paper. 

(8)  The  name  of  the  student,  the  date,  and  section  should 
be  placed  at  the  bottom  of  the  sheet  at  the  right  in  small 
letters. 

(9)  The  title  should  be  given  a  prominent  place. 

(10)  If  more  than  one  curve  is  drawn  on  the  same  paper 
for  comparison,   etc.,   use  the  same  origin  and  the  same 
abscissa  for  all.     If  more  than  one  curve  is  plotted  on  the 
same  sheet,  distinguish  the  curves  by  the  title  printed  along 
the  curve,  or  by  lines  of  different  colors. 

(11)  All  titles,  explanations,  etc.,  must  be  in  lettering, 
and  no  handwriting  should  appear  upon  the  curve  sheet. 


THE  EQUATION  OF  A  STRAIGHT  LINE 

It  is  often  desired  to  find  the  equation  that  corresponds 
to  a  given  line  (straight  or  curved)  plotted  on  squared 
paper.  In  this  course  it  will  not  be  necessary  to  obtain 
the  equation  of  a  curved  line.  A  simple  method  for  the 
equation  of  a  straight  line  follows: 

Let  APz,  Fig.  80,  be  a  line  plotted  as  usual  on  the  axes 
OX  and  OF,  and  meeting  the  axis  of  Y  at  the  point  A. 
(If  the  line  as  first  drawn,  does  not  cut  the  axis  of  Y  it  must 
be  extended  till  it  does  so.) 

At  the  point  A  draw  a  line  parallel  to  the  axis  of  X. 
Choose  any  point  on  the  line  as  P%,  and  draw  its  ordinate 
2/2-  #2  is  the  abscissa  of  this  point.  We  desire  to  obtain 
an  equation  that  will  give  us  the  relation  between  the  abscissa 
and  the  ordinate  for  this  and  every  other  point  on  this  line. 


320 


HEAT 


We  notice  first  that  the  ordinate  y2  equals  the  inter- 
cept OA  on  the  Y  axis,  plus  P2D2,  or 


Also, 


y2  =  OA+P2D2. 
yi=OA+PiDi, 

y3=OA+P3D3, 


and  so  on  for  every  point  on  the  line. 

The  value  of  the  intercept  OA  may  now  be  read  from 
the  curve.     Suppose  in  the  given  case  OA=S.     Next  read 


FIG.  80. 

from  the  curve  values  of  the  altitude  and  6a^e  of  any  tri- 
angle whose  hypothenuse  is  some  part  of  the  line  A  B.  These 
values  are  to  be  expressed  in  units  of  the  respective  scales 
used  in  plotting  X  and  Y  and  not  as  actual  lengths  in 
inches.  The  triangle  AP2D2  will  serve.  Suppose  P2D2  =  4 


and   AD2  =  W  in  the   given   case. 


P2D2 

Then  -  -  =.4. 
AD2 


But 


AD2  =  x2,  therefore,  P2D2  =  Ax2. 

If  we  had  used  other  triangles  we  should  have  obtained 
the  same  ratio  between  altitude  and  base,  and  thus, 


APPENDIX  D  321 

Or,  in  words,  we  may  now  say  that  any  ordinate  equals 
the  intercept  on  the  Y  axis  plus  .4  of  the  abscissa  for  the 
same  point.  Let  x  and  y  be  the  coordinates  of  any  point 
on  the  line  AB;  then 


which  is  the  equation  desired. 

p2/)2 

The  ratio  -     -  is  sometimes  called  the  slope  of  the  line. 
AD2 

We  may  now  state  the  general  rule  as  follows: 
RULE.     The  equation  of  a  straight  line  is  formed  by 
putting  y  equal  to  the  intercept  on  the  axis  of   Y  plus 
the  slope  times  x.     If  intercept  =  a,  and  slope  (ratio)  =  m, 
we  have, 

y  —  a-\-mx. 

NOTE.  The  student  will  notice  that  the  equation  just  given 
is  perfectly  general.  If  the  line  cuts  the  axis  of  Y  below  the  origin, 
the  intercept  will  be  a  negative  term  and  the  equation  will  be  of  the 
form  y=—a+mx.  If  the  line  slopes  so  that  an  increase  in  the 
value  of  the  abscissa  causes  a  decrease  in  the  value  of  the  ordinate, 
then  m  will  be  a  negative  quantity,  y=a—mx.  It  is  possible,  of 
course,  that  both  a  and  m  may  be  negative  at  the  same  time,  as 
y=—a—mx.  The  student  should  draw  and  consider  carefull}7 
lines  to  illustrate  each  case. 


APPENDIX  E 

FROM    PRELIMINARY   REPORT  OF  THE   POWER  TEST 
COMMITTEE  OF  THE  A.S.M.E. 

CALCULATION  OF  RESULTS 

THE  methods  to  be  followed  in  expressing  and  calculating 
those  results  which  are  not  self-evident  are  explained  as 
follows : 

(a)  Efficiency.  The  "efficiency  of  boiler,  furnace,  and  grate"  is 
the  relation  between  the  heat  absorbed  per  pound  of  coal  fired,  and  the 
calorific  value  of  one  pound  of  coal. 

The  "efficiency  of  boiler  and  furnace"  is  the  relation  between  the 
heat  absorbed  per  pound  of  combustible  burned,  and  the  calorific 
value  of  one  pound  of  combustible.  This  expression  of  efficiency 
furnishes  a  means  for  comparing  one  boiler  and  furnace  with  another, 
when  the  losses  of  unburned  coal  due  to  grates,  cleanings,  etc.,  are 
eliminated. 

The  "cpmbustible  burned"  is  determined  by  subtracting  from  the 
weight  of  coal  supplied  to  the  boiler,  the  moisture  in  the  coal,  the 
weight  of  ash  and  unburned  coal  withdrawn  from  the  furance  and 
ashpit,  and  the  weight  of  dust,  soot,  and  refuse,  if  any,  withdrawn 
from  the  tubes,  flues,  and  combustion  chambers,  including  ash  carried 
away  in  the  gases,  if  any,  determined  from  the  analyses  of  coal  and 
ash.  The  "combustible"  used  for  determining  the  calorific  value  is 
the  weight  of  coal  less  the  moisture  and  ash  found  by  analysis. 

The  "heat  absorbed"  per  pound  of  coal,  or  combustible,  is  calcu- 
lated by  multiplying  the  equivalent  evaporation  from  and  at  212  deg. 
per  Ib.  of  coal  or  combustible  by  970.4. 

(6)  Corrections  for  Moisture  in  Steam.  When  the  percentage  is  less 
than  2  per  cent  it  is  sufficient  merely  to  deduct  the  percentage  from 
the  weight  of  water  fed.  If  the  percentage  is  greater  than  2  per  cent 
pr  if  extreme  accuracy  is  required,  the  factor  of  correction  equals 


322 


APPENDIX  E  323 

in  which  Q  is  the  quality  of  the  steam  (one  minus  the  decimal  repre- 
senting the  percentage  of  moisture),  P  the  proportion  of  moisture, 
T  the  total  heat  of  water  at  the  temperature  of  the  steam,  h  the  total 
heat  of  the  feed  water,  and  H  the  total  heat  of  saturated  steam  of  the 
given  temperature. 

(c)  Correction  for  Live  Steam,  if  any,  Used  for  Aiding  Combustion. 
If  live  steam  is  admitted  into  the  furnace  or  ashpit  for  producing  blast, 
injecting  fuel,  or  aiding  combustion,  it  is  to  be  deducted  from  the 
total  evaporation,  and  the  net  evaporation  used  in  the  various  calcu- 
lations. 

(d)  Equivalent  Evaporation.     The  equivalent  evaporation  from  and 
at  212  deg.  is  obtained  by  multiplying  the  weight  of  water  evaporated, 
corrected  for  moisture  in  steam,  by  the  "factor  of  evaporation."     The 
latter  equals 

H-h 
970.4 


in  which  H  and  h  are  respectively  the  total  heat  of  saturated  steam 
and  of  the  feed  water  entering  the  boiler.  When  the  steam  is  super- 
heated, the  total  heat  of  the  steam  is  that  of  saturated  steam  plus 
the  product  of  the  number  of  degrees  of  superheating  by  the  specific 
heat  of  the  steam. 

Unless  otherwise  provided,  a  combined  boiler  and  superheater 
should  be  treated  as  one  unit,  and  the  equivalent  of  the  work  done 
by  the  superheater  should  be  included  in  the  evaporative  work  of 
the  boiler. 

(e}  Heat  Balance.  The  "heat  balance,"  or  approximate  distribution 
of  the  calorific  value  of  the  coal  or  combustible  among  the  several 
items  of  heat  utilized  and  heat  lost,  should  be  obtained  in  cases  where 
the  flue  gases  have  been  analyzed  and  a  complete  analysis  made  of 
the  coal. 

The  loss  due  to  moisture  in  the  coal  is  found  by  multiplying  the 
total  heat  of  one  pound  of  superheated  steam  at  the  temperature  of 
the  escaping  gasec,  calculated  from  the  temperature  of  the  air  in  the 
boiler  room,  by  the  proportion  of  moisture. 

The  loss  due  to  moisture  formed  by  the  burning  of  hydrogen  is 
obtained  by  multiplying  the  total  heat  of  one  pound  of  superheated 
steam  at  the  temperature  of  the  escaping  gases,  calculated  from  the 
temperature  of  the  air  in  the  boiler  room,  by  the  proportion  of  the 
hydrogen,  determined  from  the  analysis  of  the  coal,  and  multiplying 
the  result  by  9. 


324  HEAT 

The  loss  due  to  heat  carried  away  in  the  dry  gases  is  found  by 
multiplying  the  weight  of  gas  per  pound  of  coal  or  combustible  by 
the  elevation  of  temperature  of  the  gases  above  the  temperature  of 
the  boiler  room,  and  by  the  specific  heat  of  the  gases  (0.24).  The 
weight  of  gas  referred  to  is  obtained  by  finding  the  weight  of  dry 
gas  per  pound  of  carbon  burned,  using  the  formula 

11CO2+8O+7(CO+N) 
3(CO2+CO)  ' 

in  which  CO2,  CO,  O,  and  N  are  expressed  in  percentages  by  volume, 
and  multiplying  this  result  by  the  proportion  borne  by  the  carbon 
burned  to  the  whole  amount  of  coal  or  combustible  as  determined 
from  the  results  of  the  analysis  of  the  coal,  ash,  and  refuse. 

The  loss  due  to  incomplete  combustion  of  carbon  is  found  by  first 
obtaining  the  proportion  borne  by  the  carbon  monoxide  in  the  gases 
to  the  sum  of  the  carbon  monoxide  and  carbon  dioxide,  and  then 
multiplying  this  proportion  by  the  proportion  of  carbon  in  the  coal  or 
combustible,  and  finally  multiplying  the  product  by  10,150,  which  is 
the  number  of  heat  units  generated  by  burning  to  carbon  dioxide"  one 
pound  of  carbon  contained  in  carbon  monoxide. 

The  loss  due  to  combustible  matter  in  the  ash  and  refuse  is  found 
by  multiplying  the  proportion  that  this  combustible  bears  to  the 
whole  amount  of  coal  or  combustible,  by  its  calorific  value  per  pound. 
For  most  purposes  it  is  sufficient  to  assume  the  latter  to  be  14,600 
B.T.U.,  the  same  as  that  of  carbon. 

The  loss  due  to  moisture  in  the  air  is  determined  by  multiplying 
the  weight  of  such  moisture  per  pound  of  coal  or  combustible  by  the 
elevation  of  temperature  of  the  flue  gases  above  the  temperature  of 
the  boiler  room  and  by  0.47.  The  weight  of  moisture  is  found  by 
multiplying  the  weight  of  air  per  pound  of  coal  or  combustible  by  the 
moisture  in  one  pound  of  air  determined  from  readings  of  the  wet  and 
dry-bulb  thermometer. 

(/)  Total  Heat  of  Combustion  of  Coal,  by  Analysis.  The  total  heat  of 
combustion  may  be  computed  from  the  results  of  the  ultimate  analysis 
by  using  the  formula 


14,6000+62,000   H  -5-    +4000  S, 


in  which  C,  H,  O,  and  S  refer  to  the  proportions  of  carbon,  hydrogen, 
oxygen,  and  sulphur,  respectively. 


APPENDIX  E  325 

(0)  Air  for  Combustion.     The  quantity  of  air  used  may  be  calculated 
>y  the  formulae: 

3.032  N 

Lb.  of  air  per  Ib.  of  carbon  =  r,rt  .rw 

\j\Jz-r\-j\j 

Q  which  N,  CO2,  and  CO  are  the  percentages  of  dry  gas  obtained  by 
,nalysis,  and        \ 

J3.  of  air  per  Ib.  of  coal  =  lb.  air  per  Ib.  CXper  cent  C  in  the  coal. 

The  ratio  of  the  air  supply  to  that  theoretically  required  for  com- 

N 
ilete  combustion  is  N— 3782O' 


INDEX 


Absolute  Pressure,  130 

Temperature,  81 
Acetylene,  31 
Adiabatic  Expansion,  204 
Air,  Expansion  of,  83 
' '     for  Combustion,  29,  324 
"     Liquefier,  259 
"     Pumps,  146 
Alcohols,  28,  37 
Alcohol  Thermometers,  274 
Aluminum  Powder,  35 

,  Specific  Heat  of,  52 
Ammonia  Cycle,  252 
Anthracite,  28 
Anthracite  Coal,  36 
Argon,  29 
Asbestos,  234 
Ash,  27 
Atom,  10 
Autoclaves,  121 
Axis,  Coordinate,  313 

Back  Pressure,  165 
Baffle,  157 
Barnes,  H.  T.,  17 
Batteries,  6 
Benzine,  29 
Bituminous  Coal,  28 
Black  Body  Radiations,  239 
Blowers,  146 
Boiler,  36,  139,  154 

Babcock  &  Wilcox,  154 
Efficiency,  158,  235 
Horse-power,  157 
Sterling,  155 
Boiling,  Defined,  112 

Point,  106,  124 

Defined,  112 
' '     Experimentally 
determined,  115 


Bolometer,  238,  279 
Bomb  Calorimeter,  284 
Bore  of  Thermometer,  270 
Boyle's  Law,  74,  90,  203 
Brine,  249 

Bristol  Pyrometers,  279 
British  Thermal  Unit,  15 

Calculations,  311 

Calibration  of  Thermometer,  270 

Callendar,  Hugh  L.,  17 

Calorie,  15 

Calorimeters, 

Bomb,  284 
Fuel,  283,  299 
Separating,  292 
Throttling,  290 
Calorimetry,  47,  50 
Camera,  238 
Carbon,  30 

"      Dioxide,  28,  29 
' '      Monoxide,  29 
Carbureter,  9,  179 
Carnpt's  Cycle,  170 
Centigrade,  13 
Charcoal,  28,  234 
Charles'  Law,  76,  90 
Chimney,  Draft  of,  225 
Chromium,  Oxides  of,  35 
Clinker,  27,  36 
Coal,  4 

Anthracite,  36 
"      Bituminous,  28 
"     Gas,  37 
' '     Purchasing,  36 
Coke,  28 

Combustion,  Air  for,  29,  324 
Complete  Analysis,  28 
Compression    Type   of    Refriger- 
ating Plant,  247 

327 


328 


INDEX 


Compressor,  247 
Condensation,  Defined,  112 
Condenser,  119,  146,  247 

"          Alberger  Barometric, 

167 
"  Jet  or  Barometric,  163 

Surface,  163,  165 
11          Wheeler-Admiralty 

Surface,  163 
Conductance,  229 
Conduction,  223,  227 
Conductivity,  230 
Constants,  312 
Convection,  223 
Cook  Stoves,  242 
Cooling  Towers,  120 
Coordinate  Axes,  313 
Cost  Economy,  145 

11     Efficiency,  Defined,  178 
Critical  Pressure,  Defined,  114 
"       Temrerature,  107 
"  "  ,  Defined, 

114 

Crosby  Indicator,  288 
Crude  Oil,  37 
Cryogens,  257 
Curves,  313 
Cycle,  180 
"      Carnot's,  170 
"•     Rankine,  170 
Cylinder,  9    . 

Dalton's  Law,  114 
Density,  94 
Deviations,  51,  55 
Dew,  Defined,  114 

"      Point,  Defined,  113 
Dewar  Bulb,  243,  263 
Diesel  Cycle,  180 
Distillation,  118 

"          Fractional,  119 
Draft,  27 

' '    of  Chimney,  225 

Economizer,  146,  150,  160 
Effective  Pressure,  141 
Efficiency,  38 

"          of  Boilers,  158,  235 

"          "  Fuel,  158 

"  Furnace,  235 
Electrical  Equivalent  Apparatus, 

18,  21 

Electrons,  11 
Energy,  Chemical,  5 


Energy,  Defined,  1 

Diagram,  145,  148,  188, 

250 

Efficiency,  178 
Electrical,  4,  5,  6,  9 
in  Gases,  209 
Kinetic,  3 
Light,  4,  7 
Mechanical,  5 
of  Fuels   31 
"  Motion,  2 
Potential,  4 
Stream  of,  149,  152,  188 

250 

Engine,  9,  140 
"       Cycles,  211 
11       Four-cycle,  180 
Two-cycle,  180 
Entropy,  214 

Equation  of  Straight  Line,  318 
Equivalent  Evaporation,  235 
Errors,  51 
Ether  Waves,  7 
Ethylene,  29 
Evaporation,  107 

"  Defined,  112 

Factor  of,  157 
Evaporator,  249 
Exceptional  Fuels,  35 
Expansion,  Cubical,  70 

Isothermal,  74 
Joint,  65 
Linear,  67 
of  Air,  83 
' '  an  Area,  69 
' '  Gases,  74 
' '  Liquids,  71 
' '  Solids,  64 
Explosion  Engine,  37 
Explosions,  5 
Explosive  Mixtures,  191 
Explosives,  Defined,  33 
External  Work,  123 

Factor  of  Evaporation,  157 
Fahrenheit,  13 
Feed  Pump,  146 

"     Water  Heater,  Cochran,  162 
Firebox,  149 
Fireless  Cookers,  242 
Firing,  179 
Fixed  Carbon,  28 

11      Energy,  2,  4 

"      Point,  270 


INDEX 


329 


Flashlights,  35 
Fog,  Defined,  110 
Four-cycle  Engine,  180 
Freezing  Mixtures,  257 
Point,  106 

"  "      Defined,  112 

"  "      Determined,  116 

Fuel  Calorimeters,  283 
'      Efficiency,  158 
'      Energy  of,  31 
Fuels,  27 

'      Exceptional,  35 

'      Gaseous,  27,  29 

'      Liquid,  28 

'      Solid,  27 
Fulminates,  35 

Functions  of  Steam  Engine,  167 
Furnace,  36,  139 

"        Efficiency,  235 

Gas  Engine,  212 
Gas  Engine  Fuel,  178 
Gasolene,  37 
Gasolene  Engine,  9 
Gases,  Defined,  110 
Gases,  Expansion  of,  74 
Gauge  Pressure,  130 
Generators,  4,  7 
Governing,  191 
Governor,  205 

Heat  Balance,  235 

Energy,  5 

Nature  of,  8 
I  Engine,  37 

Radiation  Pyrometers,  282 

Radiations,  237 

Rays,  7 
Helium,  29 
High  Explosives,  35 
Higher  Fuel  Value,  285 
Hot  Ball,  179 
Hot  Tube,  179 

Hydro-Electric  Power  Plant,  37 
Hydrogen,  29,  30 

Sulphide,  29 

Ice,  102 

Illumination,  38 

Indicated  Horse  Power,  151,  188 

Indicator  Card,  Ideal,  171 

Insulation,  223,  234 

Devices,  242 


Insulation  of  Cold  Storage  Spaces, 

262 

Internal  Work,  123 
Ion,  118 

Iron,  Oxides  of,  35 
Isothermal  Expansion,  74,  202 

Joule,  J.  P.,  16 
Jump-spark,  179 

Kerosene,  37 
Kinetic  Energy,  3 
Theory,  10 

Latent  Heat  of  Fusion,  104 
"      "  Melting,  104 
"      ' '  Vaporization,  105, 

122 

Law,  Boyle's,  74,  90 
11     Charles',  76,  90 
Light,  237 

"      UltraViolet,  237 
"      Velocity  of,  8 
Lignite,  28 

Linear  Expansion,  67 
Liquid  Fuel,  179 
Liquids,  Defined,  109,  110 
"        Expansion  of,  71 
Low  Temperature  by  Mechanical 

Means,  258 
Lower  Fuel  Value,  285 

Magnesium,  Oxides  of,  35 

Mahler  Bomb  Calorimeter,  284 

Make  and  Break,  179 

Marks  and  Davis'  Steam  Tables, 
159 

Mass,  10 

Mean  Effective  Pressure,  141 

Measurement  of  Temperature,  268 

Mechanical  Equivalent  Appa- 
ratus, 18 

Melting,  Defined,  112 

Point,  Defined,  112 

Mercury  Thermometer,  270 

Methane,  29 

Mixtures,  117 

Method  of,  47 

Moisture,  27 

Molecules,  10 

Moorby,  N.  H.,  17 

Moore  Tubes,  240 

Motors,  4,  7 


330 


INDEX 


Natural  Gas,  37 

Newton's  Law  of  Cooling,  238 

Nitrogen,  29 

Oil,  4 

"    Engines,  179 
Optical  Pyrometers,  283 
Otto  Cycle,  180 

"     Engine,  182 
Oxidation,  4,  5 
Oxygen,  29,  30 

Piston,  9 

Peabody's  Steam  Tables,  159 
Peat,  28 
Phosphorus,  30 
Physical  Mixtures,  117 
Potential  Energy,  4 
Potentiometer,  282 
Powdered  Fuels,  29 
Power  Plant,  37 

"      Test    Committee    Report, 

230 
Pressure  Cooker,  122 

Entropy  Table,  217 
Primary  Batteries,  6 
Producer  Gas,  37,  182 
Prony  Brake,  151 
Proximate  Analysis,  28 
Pyrometer,  279,  283 
Pyrometers,  Optical,  283 

"  Heat  Radiation,  282, 

299 

Resistance,  276 
' '  Thermo- j  un  ction , 

279 

Quality  of  Steam,  Defined,  111 
Quantity  Units,  14 

Radiation,  52,  223,  236 
' '          from  Sun,  8 
Radiometer,  238 
Rankine  Cycle,  170 
Ratio  of  Specific  Heats,  201 
Rays,  Ultra  Violet,  238 
Regelation,  Defined,  112 
Regenerative  Method,  260 
Relative  Humidity,  Defined,  113 
Refrigeration,  Household,  246 
,  Mechanical,  247 
' '  Plant,    Absorption 

Type,  256 

"  "  ,  Energy  Flow 

through,  250 


Reversible  Processes,  211 
Reynolds,  Osborne,  17 
Rowland,  H.  C.,  16 

Salts,  196 

Saturation,  Defined,  110 
Saturated  Steam,  111 
Sawdust,  234 
Searles  Apparatus,  18 
Separating  Calorimeter,  292 
Significant  Figures,  309 
Solid  Defined,  109 
"     Expansion  of,  64 
' '     Fuels,  Classification  of,  28 
Solute,  117 
Solutions,  117 
Solvent,  117 
Spark,  9 

"      Plug,  179 
Specific  Heat,  44 

"      of  a  Gas,  198 
Specific  Volume,  130 
Spectroscope,  238 
Steam  Boiler  Explosion,  124 
Cycle,  252 
Dome,  146 
Engine,  4,  7,  37,  212 
Engine  Functions,  167 
Indicators,  288 
,  Quality  of,  151 
,  Saturated,  103,    106,    111, 

124,  130 
Tables,  124,  130 

"     ,  Marks  and  Davis', 

159 

"     ,  Peabody's,  159 
Temperature  of,  125,  130 
Steel,  6 

Still-heads,  119 
Stoker,  154 
Stored  Energy,  4 
Straight  Line  Equation,  318 
Stroke,  141 

Sublimation,  Defined,  112 
Sulphur,  30 

Superheated,  Defined,  111 
Steam,  111 

"       Defined,  133 
Superheaters,  146,  150 

Temperature  Absolute,  81 
"  of  Steam,  125 

Units,  12 
Thermal  Ohms,  229 


INDEX 


331 


Thermal  Resistance,  229 

Thermite,  35 

Thermo-junction,  9,  288 

' '        Pyrometers,  279 

Thermometer,  12,  51,  288 
,  Air,  87 
,  Alcohol,  274 
,  Calibration  of,  270 
,  Gas,  294 
,  Mercury,  270 
,  Sensitive,  274 
,  Standard,  272 

Thermostats,  268 

Thompson  Indicator,  288 

Three  States  of  Matter,  101 

Throttling,  191 

Calorimeter,  290 

Two-cycle  Engine,  180 

Ultimate  Chemical  Analysis,  28 
Ultra  Violet  Rays,  8 

Vacuum  Distillation,  119 
Pan,  120 


Vapor,  Defined,  110 
Tension,  124 

11     ,  Defined,  113 
Vaporization,  Defined,  112 
Vaporizer,  179 
Volatile  Matter,  28 , 
Volume,  94 


Water,  102 

"       Circulation,  146,  166 

"       Equivalent,  48 

"       Rate,  159 

"       Turbines,  4,  7 
Watts  Indicator,  151,  288 
Wave  Lengths,  237 

"      Motion,  7 
Wein's  Law,  241 
Wood,  4 
Work,  141 

"      Defined,  2 

"      External,  123 

"      Internal,  123 
Working  Medium,  195 


APPLIED  MATHEMATICS.  In  preparation  by  carefully  selected 
specialists. 

(a)  Elementary  Applied  Mathematics. 

(b)  Mathematics  for  Machinists. 

(c)  Mathematics  for  the  Woodworking  Trades. 

(d)  Mathematics  for  the  Electrical  Trades. 

(e)  Mathematics  for  the  Metal  Trades. 

THE  LOOSE  LEAF  LABORATORY  MANUAL.  A  series  of  care- 
fully selected  exercises  to  accompany  the  texts  of  the  Series,  covering 
every  subject  in  which  laboratory  or  field  work  may  be  given.  Each 
exercise  is  complete  in  itself,  and  is  printed  separately.  These  will 
be  sold  by  the  single  sheet,  or  assembled  in  any  number  and  order 
desired,  with  or  without  covers. 

The  following  are  now  ready;  others  are  in  preparation  and  will 
appear  shortly. 

(a)  Exercises  in  General  Chemistry.    By  CHARLES  M.  ALLEN, 
Head  of  Department  of  Chemistry,  Pratt  Institute.    An  intro- 
ductory course  in  Applied  Chemistry,  covering  a  year's  labora- 
tory work  on  the  acid-forming  and  metallic  elements  and 
compounds.    4to,  62  pages,  61  exercises. 

Selected  exercises,  as  desired,  to  fit  an  ordinary  binder,  two 
cents  each.     Complete,  in  paper  cover,  $1  net. 

(b)  Exercises  for  the  Applied  Mechanics  Laboratory.    By 
J.  P.  KOTTCAMP,  M.  E.,  Instructor  in  Steam  and  Strength  of 
Materials,  Pratt  Institute.    Steam,  Strength  of  Materials,  Gas 
Engines,  and  Hydraulics.    4to,  54  exercises,  with  numerous 
cuts  and  tables. 

Selected  exercises  as  desired,  to  fit  an  ordinary  binder,  two 
cents  each.     Complete,  in  paper  cover,  $1  net. 

DRAFTING  AND  DESIGN.  By  CHARLES  B.  HOWE,  Stuyvesant 
Technical  High  School,  New  York,  and  associated  specialists. 

(a)  Mechanical  Drafting. 
(6)  Engineering  Drafting. 

(c)  Agricultural  Drafting.    By  CHARLES  B.  HOWE,  Stuyvesant 

Technical  High  School,  New  York.     (In  preparation.) 

(d)  Architectural  Drafting.    By  CHARLES  B.  HOWE  and  A.  B. 

GREENBERG,  Stuyvesant  Technical  High  School,  New  York. 
(In  preparation.) 

(e)  Drafting  for  Plumbers. 

(/)  Drafting  for  Steam  Fitters. 

(g)  Electrical  Drafting. 

(k)  Drafting  for  Sheet  Metal  Workers  and  Boiler  Makers. 

(i)  Drafting  for  the  Heating  and  Ventilating  Trades. 

THE  LOOSE  LEAF  DRAWING  MANUAL.  Reference  and  Prob- 
lem Sheets  to  accompany  the  texts  in  Drafting  and  Design.  These 
will  be  furnished  singly  as  selected,  and  are  designed  to  enable  the 
instructor  to  adapt  his  instruction  closely  to  the  needs  of  his  class. 
(In  preparation.) 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

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UNIVERSITY  OF  CALIFORNIA  LIBRARY 


